## Chapter 40. Wave Functions and Uncertainty UMD Physics

Lecture 5 Operators and the SchrГ¶dinger Equation. Abstract: The ground state of a microcavity polariton Bose-Einstein condensate is determined by considering experimentally tunable parameters such as excitation density, detuning, and …, 1. Associated with any particle moving in a conservative field of force is a wave function which determines everything that can be known about the system. 2. With every physical observable q there is associated an operator Q, which when operating upon the wavefunction associated with a definite.

### Wave function and its physical significance Winner Science

Wave Functions CMU Quantum Theory Group. Wave Functions Video III.i . Variational Method: Recap We can very rarely determine exact wave functions by analytical solution of a relevant Schrödinger (wave) equation But we can always evaluate expectation values for a guess wave function Φ Variational principle for Hamiltonian operator (expectation value energy): where E 0 is the true ground-state energy Lower-limit condition: …, For a man y-particle system, its wav e function represents the propensity property of the whole system, and the modulus square of the wave function determines the probabilit y density of the.

The symbol Ψ is the wave function, a mathematical function that describes the wave-like nature of the electron. A plot of the wave function squared (Ψ2) represents an orbital, a position probability distribution map of the electron. The Schroedinger Equation in One Dimension In classical mechanics the state of motion of a particle is speciﬁed by the particle’s position and velocity. In quantum mechanics the state of motion of a particle is given by the wave function. The goal is to predict how the state of motion will evolve as time goes by. This is what the equation of motion does. The classical equation of motion is

molecule AB, the wave functions for molecular orbitals are obtained by either adding the wave functions of atomic orbitals in A and B, or by subtracting the wave function of one atom from the other, by following certain principles . wave function and has to be positive • It is important when two wavefunctions interact (see later) • It does not matter that the 2 s is represented as positive and negative in books –

molecule AB, the wave functions for molecular orbitals are obtained by either adding the wave functions of atomic orbitals in A and B, or by subtracting the wave function of one atom from the other, by following certain principles . Properties of wave functions (Text 5.1) Classical mechanics turns out to be just an approximate version of quantum mechanics. The certainties of classical mechanics are illusory,

The Schroedinger Equation in One Dimension In classical mechanics the state of motion of a particle is speciﬁed by the particle’s position and velocity. In quantum mechanics the state of motion of a particle is given by the wave function. The goal is to predict how the state of motion will evolve as time goes by. This is what the equation of motion does. The classical equation of motion is The wave function is the most fundamental concept of our most fundamental physical theory. Some explanation of what it means must be given, if only for pedagogical reasons. I shall

wave function represents the propensity property of the whole system, and the modulus square of the wave function determines the probability density of the particles appearing in … Gaussian wave packet Lecture notes The Gaussian wave function is determined by its wave function in the wave-vector space. In 1-dimensional space it is: f(k) = Aexp (k k 0)2 4 2 k ; (1) where Ais the normalization constant and k is the width of the packet in the k-space. Its graph as function of K is a bell-shaped curve centered near k 0. The normalization constant should be found from the

The wave function of a standing wave is y1x, t2 = 4.44 mm sin3132.5 rad>m2x4 sin31754 rad>s2t4. For the two traveling waves that make up this standing wave, ﬁnd the (a) amplitude; Reality of the wave function . and quantum entanglement . Mani Bhaumik1. Abstract . The intrinsic fluctuations of the underlying, immutable primary quantum fields that fill all space and time can

In wave mechanics the dynamical variable is a wave-function. This wavefunction depends on position and on time and it is a complex number – it belongs to the complex numbers C (we denote the real numbers by R). When all three dimensions of space are relevant we write the wavefunction as . Ψ(ix, t) ∈ C . (1.1) When only one spatial dimension is relevant we write it as Ψ(x, t) ∈ C. The The State of the No-Boundary Wave Function Stephen Hawking, DAMTP, Cambridge Thomas Hertog, Universiteit Leuven Hawking70, Cambridge, January 7, 2012 James Hartle, UCSB, SantaBarbara based on work with . If the universe is a quantum mechanical Ψ system it has a quantum state. What is it? A Quantum Universe A theory of the quantum state is the objective of Quantum Cosmology. No State - …

Gaussian wave packet Lecture notes The Gaussian wave function is determined by its wave function in the wave-vector space. In 1-dimensional space it is: f(k) = Aexp (k k 0)2 4 2 k ; (1) where Ais the normalization constant and k is the width of the packet in the k-space. Its graph as function of K is a bell-shaped curve centered near k 0. The normalization constant should be found from the Direction of Wave Propagation If we know shape of the pulse at an instant time, or propagation direction of the particles of the pulse we can find the direction of wave propagation. Example: Given picture below shows the direction of wave propagation. Find the …

What determines the angular frequency in a wave function. determine the wave functions of investment portfolios and demonstrate how portfolio wave functions based on returns data for the FTSE All Share Index are strongly compatible with the …, The function in figure 5.14(b) is not single-valued, so it cannot be a wave function. The function in figure 5.14(c) does not satisfy the condition for a continuous first derivative, so it cannot be a wave function..

### How to determine the direction of a wave propagation

Lecture 5 Operators and the SchrГ¶dinger Equation. The function in figure 5.14(b) is not single-valued, so it cannot be a wave function. The function in figure 5.14(c) does not satisfy the condition for a continuous first derivative, so it cannot be a wave function., The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0. Phase is a frequency domain or Fourier transform domain concept, and as such, can be readily understood in terms of simple....

Quantum Mechanics/Meaning of Quantum Wave Function. Reality of the wave function . and quantum entanglement . Mani Bhaumik1. Abstract . The intrinsic fluctuations of the underlying, immutable primary quantum fields that fill all space and time can, sinusoidal wave as being localized in some place. Indeed, the positions for these two wave- Indeed, the positions for these two wave- functions are ill-deﬁned, so ….

### 2. Wavefunctions Weber State University

Consciousness and the Collapse of the Wave Function. What Determines Whether a Wave Function Is Inherently Necessary? Allen C. Dotson 1 Received August 10, 1990; revised January 31, 1991 The inherent necessity of wave functions may be determined in either of two ways. One way, frequently presupposed, states that the fundamental validity of wave fimctions is determined generically: The nature of the system determines the assignability of 16/01/2009 · Best Answer: In quantum mechanics, the wave function is a mathematical quantity that describes a particle (like an electron). To be specific, the wave function determines the probabilities related to a particle's position, momentum, and other physical properties..

The Schroedinger Equation in One Dimension In classical mechanics the state of motion of a particle is speciﬁed by the particle’s position and velocity. In quantum mechanics the state of motion of a particle is given by the wave function. The goal is to predict how the state of motion will evolve as time goes by. This is what the equation of motion does. The classical equation of motion is On the reality and meaning of the wave function Shan Gao February 19, 2014 1 Introduction The physical meaning of the wave function is an important interpretative prob-

The wave function helps predict the results of quantum experiments with incredible accuracy. But it describes a world where particles have fuzzy properties – for example, existing in two places Notice that AGP wave-function is similar to the Gutzwiller BCS wave function used on lattice system . The full JAGP wave-function is defined by the product of different terms, namely one-body, two-body, three-body Jastrow and an antisymmetric part ( ).

sinusoidal wave as being localized in some place. Indeed, the positions for these two wave- Indeed, the positions for these two wave- functions are ill-deﬁned, so … 2.1. GENERAL SOLUTION TO WAVE EQUATION 1 I-campus project School-wide Program on Fluid Mechanics Modules on Waves in ßuids T.R.Akylas&C.C.Mei CHAPTER TWO

For , there is one energy and only one wave function . For , there is one energy and four possible states, corresponding to the following allowable values of and Thus, there are four wave functions , , … One of the most profound and mysterious principles in all of physics is the Born Rule, named after Max Born. In quantum mechanics, particles don’t have classical properties like “position” or “momentum”; rather, there is a wave function that assigns a (complex) number, called the “amplitude,” to each possible measurement outcome.

Thus, given the frequency and wave number of a wave function, we can determine the speed of the particle from the phase velocity of its wave function, v = 2vp. We could also try to learn from the wave function the position of the particle. However, the wave function above tells us nothing about where the particle is to be found in space. We can make this statement because this wave function is Wave function, in quantum mechanics, variable quantity that mathematically describes the wave characteristics of a particle. The value of the wave function of a particle at a given point of space and time is related to the likelihood of the particle’s being there at the time.

The wave function of a photon is a topic that has for long been ignored since the physicists have been primarily interested in emission and absorption processes, for On the reality and meaning of the wave function Shan Gao February 19, 2014 1 Introduction The physical meaning of the wave function is an important interpretative prob-

the cosine functions with diﬀerent values of k, i.e., with diﬀerent wavelengths. In other In other words, A(k) gives the distribution of wave numbers kthat make up the wave packet. equation determines ψ(x, t) for all t. However, note that wavefunction collapse upon However, note that wavefunction collapse upon measurement is not deterministic!

determine the wave functions of investment portfolios and demonstrate how portfolio wave functions based on returns data for the FTSE All Share Index are strongly compatible with the … Wave function is defined as that quantity whose variations make up matter waves. It is represented by Greek symbol ψ(psi), ψ consists of real and imaginary parts. It is represented by Greek symbol ψ(psi), ψ consists of real and imaginary parts.

The wave function for a single electron, also called a wave packet, is created by combin- ing many wave functions with different wavelengths, where the wavelength is deter- … Reality of the wave function . and quantum entanglement . Mani Bhaumik1. Abstract . The intrinsic fluctuations of the underlying, immutable primary quantum fields that fill all space and time can

## Wave function of the Universe UCSB Physics

Phase (waves) Physics Problems and Solutions FANDOM. 12/08/2011 · The change in wavelength determines the amount of change in energy of an EM wave. (Photon) Double the frequency (half the wavelength) and you double the energy. (Photon) Double the frequency (half the wavelength) and you double the energy., The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0. Phase is a frequency domain or Fourier transform domain concept, and as such, can be readily understood in terms of simple....

### Physics 107 Problem 5.1 O. A. Pringle

The Wave Function Department of Physics and Astronomy. Abstract. The inherent necessity of wave functions may be determined in either of two ways. One way, frequently presupposed, states that the fundamental validity of wave functions is determined generically: The nature of the system determines the assignability of inherently necessary wave functions., CHAPTER II The Wave Function and Probability In the last chapter, we examined some of the arguments that lead scientists in the first years of the 1900's to conclude that light was actually composed of individual elements called.

2.1. GENERAL SOLUTION TO WAVE EQUATION 1 I-campus project School-wide Program on Fluid Mechanics Modules on Waves in ßuids T.R.Akylas&C.C.Mei CHAPTER TWO wave function as a description of real physical wave. But this view met serious objections and was soon replaced by Born’s probability interpretation (Born 1926), which becomes the standard interpretation of the wave function today. According to this interpretation, the wave function is a probability amplitude, and the square of its absolute value represents the probability density for a

Two wave functions ˚(x) and (x) which are orthogonal to each other, h˚j i = 0, represent mutually exclusive physical states: if one of them is true, in the sense that it is a correct description of the quantum system, the other is false, that is, an incorrect description of the quantum system. wave function as a description of real physical wave. But this view met serious objections and was soon replaced by Born’s probability interpretation (Born 1926), which becomes the standard interpretation of the wave function today. According to this interpretation, the wave function is a probability amplitude, and the square of its absolute value represents the probability density for a

What Determines Whether a Wave Function Is Inherently Necessary? Allen C. Dotson 1 Received August 10, 1990; revised January 31, 1991 The inherent necessity of wave functions may be determined in either of two ways. One way, frequently presupposed, states that the fundamental validity of wave fimctions is determined generically: The nature of the system determines the assignability of Ontology and the Wave Function Collapse Armin Nikkhah Shirazi∗ University of Michigan Ann Arbor, MI 48109 February 7th, 2011 Abstract This paper makes a case for ontology, the study of existence, to be explicitly and formally incorporated

The wave function of a standing wave is y1x, t2 = 4.44 mm sin3132.5 rad>m2x4 sin31754 rad>s2t4. For the two traveling waves that make up this standing wave, ﬁnd the (a) amplitude; The State of the No-Boundary Wave Function Stephen Hawking, DAMTP, Cambridge Thomas Hertog, Universiteit Leuven Hawking70, Cambridge, January 7, 2012 James Hartle, UCSB, SantaBarbara based on work with . If the universe is a quantum mechanical Ψ system it has a quantum state. What is it? A Quantum Universe A theory of the quantum state is the objective of Quantum Cosmology. No State - …

1. Associated with any particle moving in a conservative field of force is a wave function which determines everything that can be known about the system. 2. With every physical observable q there is associated an operator Q, which when operating upon the wavefunction associated with a definite wave function represents the propensity property of the whole system, and the modulus square of the wave function determines the probability density of the particles appearing in …

2.1. GENERAL SOLUTION TO WAVE EQUATION 1 I-campus project School-wide Program on Fluid Mechanics Modules on Waves in ßuids T.R.Akylas&C.C.Mei CHAPTER TWO Abstract. The inherent necessity of wave functions may be determined in either of two ways. One way, frequently presupposed, states that the fundamental validity of wave functions is determined generically: The nature of the system determines the assignability of inherently necessary wave functions.

Wave function, in quantum mechanics, variable quantity that mathematically describes the wave characteristics of a particle. The value of the wave function of a particle at a given point of space and time is related to the likelihood of the particle’s being there at the time. determine the wave functions of investment portfolios and demonstrate how portfolio wave functions based on returns data for the FTSE All Share Index are strongly compatible with the …

Reality of the wave function . and quantum entanglement. Mani Bhaumik1 Department of Physics and Astronomy, University of California, Los Angeles, USA.90095. Abstract . The intrinsic fluctuations of the underlying, immutable quantum fields that fill all space and time can the support element of reality of a wave function in quantum mechanics. The mysterious non-locality of quantum entanglement Chapter 40. Wave Functions and Uncertainty The wave function Chapter 40.. Wave Functions and Uncertainty Topics: •Waves, Particles, and the Double‐Slit Experiment •Connecting the Wave and Photon Views •The Wave Function •Normalization •Wave Packets •The Heisenberg Uncertainty Principle. Review double slit. Connecting the Wave and Photon Views The intensity of the light wave

4.1 Fourier Series for Periodic Functions 321 Example 2 Find the cosine coeﬃcients of the ramp RR(x) and the up-down UD(x). Solution The simplest way is to start with the sine series for the square wave: a function whose purpose in life is to be integrated. In order for the rule to work, In order for the rule to work, however, we must impose the condition that the total probability of nding the

The wave function gradually narr ows as R s de- creases from 3 to 0.8, and it shows a drastic change to have a sharp peak at r = 0 for R s . 0 . 7, i.e., in the pho- Two wave functions ˚(x) and (x) which are orthogonal to each other, h˚j i = 0, represent mutually exclusive physical states: if one of them is true, in the sense that it is a correct description of the quantum system, the other is false, that is, an incorrect description of the quantum system.

Notice that AGP wave-function is similar to the Gutzwiller BCS wave function used on lattice system . The full JAGP wave-function is defined by the product of different terms, namely one-body, two-body, three-body Jastrow and an antisymmetric part ( ). 12/08/2011 · The change in wavelength determines the amount of change in energy of an EM wave. (Photon) Double the frequency (half the wavelength) and you double the energy. (Photon) Double the frequency (half the wavelength) and you double the energy.

The symbol Ψ is the wave function, a mathematical function that describes the wave-like nature of the electron. A plot of the wave function squared (Ψ2) represents an orbital, a position probability distribution map of the electron. Wave function, in quantum mechanics, variable quantity that mathematically describes the wave characteristics of a particle. The value of the wave function of a particle at a given point of space and time is related to the likelihood of the particle’s being there at the time.

Standing Waves 3 In this equation, v is the (phase) velocity of the waves on the string, ‚ is the wavelength of the standing wave, and f is the resonant frequency for the standing wave. the cosine functions with diﬀerent values of k, i.e., with diﬀerent wavelengths. In other In other words, A(k) gives the distribution of wave numbers kthat make up the wave packet.

Standing Waves 3 In this equation, v is the (phase) velocity of the waves on the string, ‚ is the wavelength of the standing wave, and f is the resonant frequency for the standing wave. For the antisymmetric wave function, the particles are most likely to be found far away from each other. In fact, there is zero probability that they will be found at the same spot, because if ψ ( x 1 , x 2 ) = − ψ ( x 2 , x 1 ) , obviously ψ ( x , x ) = 0.

wave function of the universe, or the universal wave function. The wave functions The wave functions of the subsystems are thought to be derivative of the universal one. The wave function of a standing wave is y1x, t2 = 4.44 mm sin3132.5 rad>m2x4 sin31754 rad>s2t4. For the two traveling waves that make up this standing wave, ﬁnd the (a) amplitude;

### WAVE EQUATIONS WAVE FUNCTIONS AND ORBITALS

Meaning of the wave function arXiv. The wave function gradually narr ows as R s de- creases from 3 to 0.8, and it shows a drastic change to have a sharp peak at r = 0 for R s . 0 . 7, i.e., in the pho-, The wave function for a single electron, also called a wave packet, is created by combin- ing many wave functions with different wavelengths, where the wavelength is deter- ….

### Energy in waves (Amplitude and Frequency) Physics Forums

Consciousness and the Collapse of the Wave Function. What Determines Whether a Wave Function Is Inherently Necessary? Allen C. Dotson 1 Received August 10, 1990; revised January 31, 1991 The inherent necessity of wave functions may be determined in either of two ways. One way, frequently presupposed, states that the fundamental validity of wave fimctions is determined generically: The nature of the system determines the assignability of The State of the No-Boundary Wave Function Stephen Hawking, DAMTP, Cambridge Thomas Hertog, Universiteit Leuven Hawking70, Cambridge, January 7, 2012 James Hartle, UCSB, SantaBarbara based on work with . If the universe is a quantum mechanical Ψ system it has a quantum state. What is it? A Quantum Universe A theory of the quantum state is the objective of Quantum Cosmology. No State - ….

Ontology and the Wave Function Collapse Armin Nikkhah Shirazi∗ University of Michigan Ann Arbor, MI 48109 February 7th, 2011 Abstract This paper makes a case for ontology, the study of existence, to be explicitly and formally incorporated Standing Waves 3 In this equation, v is the (phase) velocity of the waves on the string, ‚ is the wavelength of the standing wave, and f is the resonant frequency for the standing wave.

The wave function of a standing wave is y1x, t2 = 4.44 mm sin3132.5 rad>m2x4 sin31754 rad>s2t4. For the two traveling waves that make up this standing wave, ﬁnd the (a) amplitude; One of the most profound and mysterious principles in all of physics is the Born Rule, named after Max Born. In quantum mechanics, particles don’t have classical properties like “position” or “momentum”; rather, there is a wave function that assigns a (complex) number, called the “amplitude,” to each possible measurement outcome.

in which we may take ω = kc. The first term represents a wave propagating in the positive x-direction since it is a function of x − ct only; the second term, being a function of x + ct, represents a wave propagating in the negative x-direction. Wave Functions Video III.i . Variational Method: Recap We can very rarely determine exact wave functions by analytical solution of a relevant Schrödinger (wave) equation But we can always evaluate expectation values for a guess wave function Φ Variational principle for Hamiltonian operator (expectation value energy): where E 0 is the true ground-state energy Lower-limit condition: …

Whether the wave function is symmetric or antisymmetric under such operations gives you insight into whether two particles can occupy the same quantum state. Given that P ij 2 = 1, note that if a wave function is an eigenfunction of P ij , then the possible eigenvalues are 1 and –1. Direction of Wave Propagation If we know shape of the pulse at an instant time, or propagation direction of the particles of the pulse we can find the direction of wave propagation. Example: Given picture below shows the direction of wave propagation. Find the …

The 4 Quantum Numbers (QN’s), Their Rules, and Their Roles QN Name Allowed Values What It Determines n principal 1, 2, 3, Orbital: A wave function with a given value of n, l, and ml Subshell or Sublevel: A set of orbitals with the same values of n and l (ml can be anything) Shell: A set of orbitals with the same value of n (l and ml can be anything) ms spin +½, -½ Orientation of an likes wave, and thus a wave function is used to describe them. Schrödinger originally regarded the wave function as a description of real physical wave. But this view met serious objections and was soon replaced by Born’s probability interpretation (Born 1926), which becomes the standard interpretation of the wave function today. According to this interpretation, the wave function is a

Notice that AGP wave-function is similar to the Gutzwiller BCS wave function used on lattice system . The full JAGP wave-function is defined by the product of different terms, namely one-body, two-body, three-body Jastrow and an antisymmetric part ( ). Chapter 4 Polarization 4.1 Introduction Polarization generally just means “orientation.” It comes from the Greek word polos, for the axis of a spinning globe. Wave polarization occurs for vector fields. For light (electromagnetic waves) the vectors are the electric and magnetic fields, and the light’s polarization direction is by convention along the direction of the electric field

Standing Waves 3 In this equation, v is the (phase) velocity of the waves on the string, ‚ is the wavelength of the standing wave, and f is the resonant frequency for the standing wave. sinusoidal wave as being localized in some place. Indeed, the positions for these two wave- Indeed, the positions for these two wave- functions are ill-deﬁned, so …

a function whose purpose in life is to be integrated. In order for the rule to work, In order for the rule to work, however, we must impose the condition that the total probability of nding the wave function represents the propensity property of the whole system, and the modulus square of the wave function determines the probability density of the particles appearing in …

For a man y-particle system, its wav e function represents the propensity property of the whole system, and the modulus square of the wave function determines the probabilit y density of the The wave function is the most fundamental concept of our most fundamental physical theory. Some explanation of what it means must be given, if only for pedagogical reasons. I shall

Chapter 4 Polarization 4.1 Introduction Polarization generally just means “orientation.” It comes from the Greek word polos, for the axis of a spinning globe. Wave polarization occurs for vector fields. For light (electromagnetic waves) the vectors are the electric and magnetic fields, and the light’s polarization direction is by convention along the direction of the electric field Ontology and the Wave Function Collapse Armin Nikkhah Shirazi∗ University of Michigan Ann Arbor, MI 48109 February 7th, 2011 Abstract This paper makes a case for ontology, the study of existence, to be explicitly and formally incorporated

determine the wave functions of investment portfolios and demonstrate how portfolio wave functions based on returns data for the FTSE All Share Index are strongly compatible with the … What Determines Whether a Wave Function Is Inherently Necessary? Allen C. Dotson 1 Received August 10, 1990; revised January 31, 1991 The inherent necessity of wave functions may be determined in either of two ways. One way, frequently presupposed, states that the fundamental validity of wave fimctions is determined generically: The nature of the system determines the assignability of

In wave mechanics the dynamical variable is a wave-function. This wavefunction depends on position and on time and it is a complex number – it belongs to the complex numbers C (we denote the real numbers by R). When all three dimensions of space are relevant we write the wavefunction as . Ψ(ix, t) ∈ C . (1.1) When only one spatial dimension is relevant we write it as Ψ(x, t) ∈ C. The 28 WAVE FUNCTION OF THE UNIVERSE 2961 sending t—+ — i~ and adjusting the sign so that it is posi-tive. In cases where there is a well-defined time and a corre-

Gaussian wave packet Lecture notes The Gaussian wave function is determined by its wave function in the wave-vector space. In 1-dimensional space it is: f(k) = Aexp (k k 0)2 4 2 k ; (1) where Ais the normalization constant and k is the width of the packet in the k-space. Its graph as function of K is a bell-shaped curve centered near k 0. The normalization constant should be found from the Whether the wave function is symmetric or antisymmetric under such operations gives you insight into whether two particles can occupy the same quantum state. Given that P ij 2 = 1, note that if a wave function is an eigenfunction of P ij , then the possible eigenvalues are 1 and –1.

Reality of the wave function . and quantum entanglement . Mani Bhaumik1. Abstract . The intrinsic fluctuations of the underlying, immutable primary quantum fields that fill all space and time can Direction of Wave Propagation If we know shape of the pulse at an instant time, or propagation direction of the particles of the pulse we can find the direction of wave propagation. Example: Given picture below shows the direction of wave propagation. Find the …

In the classical picture, we usually work with the position and momentum of a particle or particles. From these, we can generate all the physical information about the system. However, it is easy to see how such an approach will run into serious problems for quantum mechanics. If we consider, for Here is (in my opinion) an easier answer. I'm sure you know that the line y = x crosses the x-axis in the origin (0, 0). Now we shift the entire line to the right in such a …

12/08/2011 · The change in wavelength determines the amount of change in energy of an EM wave. (Photon) Double the frequency (half the wavelength) and you double the energy. (Photon) Double the frequency (half the wavelength) and you double the energy. In the simple case of motion in one dimension, I get that the wave function is composed of a complex vector rotating about the time axis; and that...

Wave function is defined as that quantity whose variations make up matter waves. It is represented by Greek symbol ψ(psi), ψ consists of real and imaginary parts. It is represented by Greek symbol ψ(psi), ψ consists of real and imaginary parts. 28 WAVE FUNCTION OF THE UNIVERSE 2961 sending t—+ — i~ and adjusting the sign so that it is posi-tive. In cases where there is a well-defined time and a corre-

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