A complex scalar field that describes a quantum mechanical system. The square of the modulus of the wave function gives the probability of the system to be found in a particular state.

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62 views

Tip of a spreading wave-packet: asymptotics beyond all orders of a saddle point expansion

This is a technical question coming from mapping of an unrelated problem onto dynamics of a non-relativistic massive particle in 1+1 dimensions. This issue is with asymptotics dominated by a term ...
6
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3answers
1k views

Electrons - What is Waving?

If an electron is a wave, what is waving? So many answers on the internet say "the probability that a particle will be at a particular location"... so... the electron is a physical manifestation of ...
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2answers
396 views

Is the electron wave function defined during photon emission

I have heard the term quantum leap to describe the (instantaneous?) transition from a higher energy orbital to a lower energy orbital. Yet, I understand that this transition time has now been ...
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3answers
240 views

Time Varying Potential, series solution

Suppose we have a time varying potential $$\left( -\frac{1}{2m}\nabla^2+ V(\vec{r},t)\right)\psi = i\partial_t \psi$$ then I want to know why is the general solution written as $\psi = ...
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1k views

How to calculate ground state wave function?

I have seen many ground state wave functions. From where are they derived? How can one calculate them? Where can one find a list of all ground state wavefunctions discovered?
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1answer
492 views

Solving Schrödinger's equation for a specific potential

I am trying to solve this differential equation: $$-\chi''(\epsilon)+\Big[\epsilon^2+\frac{2F}{hw}\sqrt{\frac{h}{hw}}\epsilon \Big]\chi(\epsilon)=\mu\chi(\epsilon) \tag1$$ This was found ...
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2answers
1k views

Matter waves and de Broglie wave length

The wavelength of a particle of momentum p is calculated using De Broglie relation. The de Broglie relation was postulated for what is called a matter waves. Now according to the statistical ...
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1answer
627 views

Wave function of hydrogen atom including spin of nucleus

How do I write the wave function of hydrogen atom taking into consideration of nucleus spin? For example consider $2S_{\frac{1}{2}}$ state with nucleus spin $I$, then wave function ...
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3answers
600 views

One dimensional Schrödinger equation equation with initial condition, finding the probability of the particle's future position

A particle of mass $m$ moves freely in the interval $[0,a]$ on the $x$ axis. Initially the wave function is: $$f(x)=\frac{1}{\sqrt{3}}\operatorname{sin}\Big( \frac{\pi x}{a} ...
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2answers
2k views

Relation between wavenumber and propagation constant

What is the exact difference between wavenumber and propagation constant in an electromagnetic wave propagating in a medium such as a transmission line, cause i am a bit confused. Does it have to do ...
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1answer
91 views

How are particle simplices associated into complex particles?

Nonfundamental particles are seen as made up of fundamental particles (in whatever specific theory). consider the simple case of 2 simplex particles (subscript 1 and 2) which form a complex particle ...
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2answers
226 views

Expressing a particle's matter wave in terms of its momentum

I'm following Zettili's QM book and on p. 39 the following manipulation is done, Given a localized wave function (called a wave packet), it can be expressed as $$\psi(x,t) = \frac{1}{\sqrt{ 2 \pi}} ...
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3answers
967 views

Smoothness constraint of wave function

Is there anything in the physics that enforces the wave function to be $C^2$? Are weak solutions to the Schroedinger equation physical? I am reading the beginning chapters of Griffiths and he doesn't ...
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1answer
2k views

How to calculate time evolution of a wave function in an 1D infinite square well potential?

A particle in an infinite square well has an initial wavefunction $$\psi (x,0) ~=~ Ax(a-x) \qquad \mathrm{for}\qquad 0\leq x\leq a.$$ Now the question is to calculate $\psi (x,t)$. I have ...
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1answer
3k views

What does $\Psi^*$ mean in Schrodinger's formulation of Quantum Mechanics?

I am not a physics student. In one of my courses, some fundamental concepts of Quantum mechanics were needed, so I was going through them when I stumbled upon this. It says $$\text{probability} = ...
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4answers
536 views

How can I show that an arbitrary wavefunction in a 1D SHO is periodic in time?

I want to show that an arbitrary wavefunction $f$ in a one dimensional harmonic potential reproduces itself after a period T up to a phase factor: $f(x,t+T)=Af(x,t)$, $|A|=1$ I am not sure if this ...
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3answers
400 views

What is the rationale behind representing a state function by a complex valued function in QM?

What is the rationale behind representing a state function of an electron with a complex valued function $\Psi$. If only the probabilistic argument was required then why not represent it with just a ...
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1answer
656 views

Plotting Hydrogen's $2P_{x,y,z}$ Probability Densities in MATLAB [closed]

I have spent an unreasonable amount of time trying to plot $F(r,\theta,\phi)$ plane slices in MATLAB. I want to look at $x-y,y-z,x-z$ planes. Here's the function, specifically: ...
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1answer
496 views

Ground state energies with fermions of same spin?

Consider two non-interacting Fermions (half-integer spin) confined in a 'box'. Construct the anti-symmetric wavefunctions and compare the corresponding ground-state energies of the two systems; ...
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1answer
554 views

Transmission and reflection

What is the transmission amplitude of a wavefunction $\phi(x)=e^{ikx}(\tanh x -ik)$? I would have thought that it is $\tanh x -ik$ since this is the factor associated with the forward travelling ...
3
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1answer
192 views

Expected value inequality

Why is $\langle p^2\rangle >0$ where $p=-i\hbar{d\over dx}$, (noting the strict inequality) for all normalized wavefunctions? I would have argued that because we can't have $\psi=$constant, but ...
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2answers
3k views

Speed of a particle in quantum mechanics: phase velocity vs. group velocity

Given that one usually defines two different velocities for a wave, these being the phase velocity and the group velocity, I was asking their meaning for the associated particle in quantum mechanics. ...
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4answers
238 views

Are Everettian branchings global or local?

Everett's theory of quantum mechanics is about the wavefunction of the whole universe holistically. If a branching occurs very far away at the Andromeda galaxy, do I also branch? Are branchings global ...
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1answer
529 views

Weird operator and wavefunctions

How can one show that $\int_{-\infty}^{\infty}\psi^*(x)(d/dx+\tanh x)(-d/dx+\tanh x)\psi(x) dx=\int_{-\infty}^{\infty} |(d/dx+\tanh x)\psi(x)|^2 dx$, where $\psi$ is normalized?
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1answer
1k views

Probability current

Conservation of probability: Suppose a wavefunction has ${\partial \mathbb P \over \partial t} = -t f(x,t)$ and ${\partial j \over \partial x} = i f(x,t)$. How does it follow that ${\partial \mathbb P ...
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1answer
245 views

Young's double slit

Am I right to think the (general) probability distribution of photon in a double slit experiment at the screen has the form $|\psi|^2 = c e^{\alpha x^2}\cos^2(\beta x)$? (Due to the superposition of ...
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1answer
663 views

Superposition of wavefunctions

Suppose you have 2 normalized wavefunctions $\psi_1=Ne^{iax}e^{if(x)}e^{i\omega t}$ and $\psi_2=Ne^{-iax}e^{if(x)}e^{i\omega t}$ defined on $x\in [-x_0,x_0]$ and vanishes for $|x|>x_0$. What then ...
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1answer
514 views

Simple rotation of an atomic orbital wavefunction

We know that an atomic orbital wavefunction may be written in terms of polar coordinates, $$\psi (r, \theta, \phi) = R(r) A(\theta, \phi)$$ where $R(r)$ is the radial component and $A(\theta, \phi)$ ...
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0answers
115 views

Spin 1/2 finite-difference field simulator?

Is there a finite-difference field simulator for spin 1/2 fields, something like meep for electromagnetism (spin 1)? Looking for something free (GNU, MIT or other open/free style license) and easy ...
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1answer
347 views

Sudden change in the Hamiltonian

Could someone explain what this sentence mean? "If the Hamiltonian changes suddenly by a finite amount, the wavefunction must change continuously in order that the time-dependent Schrodinger equation ...
4
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1answer
291 views

Projection of states after measurement

Continuing from the my previous 2-state system problem, I am told that the observable corresponding to the linear operator $\hat{L}$ is measured and we get the +1 state. Then it asks for the ...
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2answers
645 views

Plotting a wave function that represents a particle

The problem is this: A particle is represented by the wave function $\psi = e^{-(x-x_{0})^2/2\alpha}\sin kx$. Plot the wave function $\psi$ and the probability distribution $|\psi(x)|^2$. This ...
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2answers
322 views

Schematic expression of the Schrodinger equation

it would be great if someone could help me understand the following quote regarding wavefunctions :) "$$\psi(x)=\sum_n C_nu_n(x)+\int dE C(E)u_E(x)$$ The expression is schematic because we have ...
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1answer
465 views

Determining wave function for term symbol 1D

I am trying to follow a book (Introduction to Ligand Field Theory by Ballhausen in 1962 on pg 15), but it isn't clear how they make a particular leap. Background I want to find the wave function for ...
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4answers
586 views

Is the wave function objective or subjective?

Here is a question I am curious about. Is the wave function objective or subjective, or is such a question meaningless? Conventionally, subjectivity is as follows: if a quantity is subjective then ...
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3answers
737 views

Historical background of wave function collapse

I wonder what were the main experiments that led people to develop the concept of wave function collapse? (I think I am correct in including the Born Rule within the general umbrella of the collapse ...
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1answer
984 views

Confusion between the de Broglie wavelength of a particle and wave packets

So I learned that the de Broglie wavelength of a particle, $\lambda = \frac{h}{p}$, where h is Planck's constant and p is the momentum of the particle. I also learned that a quantum mechanics ...
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1answer
270 views

Help me to visualize this wave equation in time, to which direction it moves?

The wave is $\bar{E} = E_{0} sin(\frac{2\pi z}{\lambda} + wt) \bar{i} + E_{0} cos(\frac{2 \pi z}{\lambda}+wt) \bar{j}$ Let's simplify with $z = 1$. Now the xy-axis is defined by parametrization ...
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1answer
771 views

Simple Quantum Mechanics question about the Free particle, (part1)

I am reading Introduction to Quantum Mechanics by David Griffiths and I am in Ch2 page 59. He starts out writing the time dependent Schrödinger equation and the solution for $\psi(x,t)$ for the free ...
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1answer
2k views

Wavefunction normalization

How do we normalize a wavefunction that's a linear combination of sines and cosines (or of $Ae^{ikx}+Be^{-ikx}$ -- they're the same, right)? One you square it, wouldn't the integrand be oscillating ...
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6answers
1k views

Is there a direct physical interpretation for the complex wavefunction?

The Schrodinger equation in non-relativistic quantum mechanics yields the time-evolution of the so-called wavefunction corresponding to the system concerned under the action of the associated ...
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11answers
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About the complex nature of the wave function?

1. Why is the wave function complex? I've collected some layman explanations but they are incomplete and unsatisfactory. However in the book by Merzbacher in the initial few pages he provides an ...
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2answers
188 views

fermions and quantum gates

Say that I have 2 qubits - 2 spin half fermions. my initial condition is $|00\rangle$ in the spin-wave function and some anti-symmetrical spacial wave function. I'm wondering about what happens when ...
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3answers
2k views

What is the relation between position and momentum wavefunctions in quantum physics?

I have read in a couple of places that $\psi(p)$ and $\psi(q)$ are Fourier transforms of one another (e.g. Penrose). But isn't a Fourier transform simply a decomposition of a function into a sum or ...