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.

learn more… | top users | synonyms

7
votes
1answer
699 views

Must the derivative of the wave function at infinity be zero?

I came across a problem in Griffiths where the derivative of the wave function (with respect to position in one dimension) evaluated at $\pm\infty$ is zero. Why is this? Is it true for any function ...
4
votes
1answer
384 views

Help me understand the first equation in Landau & Lifshitz's Quantum Mechanics

While I've covered a basic course in Quantum Mechanics, I'm self-studying Landau & Lifshitz's book to help me understand what's going on. Unfortunately, I'm stuck on the very first equation in ...
1
vote
1answer
2k views

what is phase angle of wave function $\phi \,$?

this is wave function: $$\Psi{(\vec r, t)}=\Psi_0 e^{i(\vec k \cdot \vec r-\omega t)}$$ $$\Psi{(\vec r, t)}=A e^{i(\phi + \vec k \cdot \vec r-\omega t)}$$. what is phase angle $\phi$ of wave ...
1
vote
1answer
479 views

How Represent Waves via Complex Numbers?

i try to finished my thesis, (Just have a problem with the wave mechanics) this is wave function: $$\Psi(\vec x, t)=A\exp{i(\phi+\vec k.\vec x-\omega t)}$$ In mathematics, the symbol $i$ is ...
1
vote
1answer
517 views

How Light or Water Intensity is equal to square modulus of wave function of Light or Water Waves $I=|\psi|^2 \,$?

I've seen the Wave Function as a psi $\Psi$ $\psi$. And always heard that the wave function is the Complex Number as Imaginary and real number. But I've never seen it I've never seen components of ...
1
vote
2answers
316 views

matter wave and wave function

Is there any mathematical relationship between matter wave (or de Broglie wave) and wave function? Also, does each type of particle (e.g. photon, electron, positron etc.) have its own unique wave ...
2
votes
1answer
2k views

Angular momentum operator and expectation values

I was reading some notes and it says that $\langle L_z^2\rangle=\langle L^2\rangle$ IFF the system is radially symmetric. I can see that in order that the LHS of the statement implies that $\langle ...
1
vote
1answer
591 views

Relationship between classical electromagnetic wave frequency and quantum wave function + de broglie frequency

As it is. As I study through classical mechanics and quantum mechanics, I began to wonder whether there is a relationship between classical electromagnetic wave frequency and quantum wave function ...
0
votes
1answer
487 views

Wave packets v.s. wave trains

Could someone please explain the difference between a wave packet and a wave train? I have rummaged around online but have not been able to find a definitive definition.
1
vote
3answers
629 views

Why can't we know the speed, $\vec{v}(t)$, and position, $\vec{r}(t)$, of an electron (the two) at the same time $t$?

I've read something about this and I conclude that it happens because of the uncertainty principle. But I don't understand very well the meaning of that. I mean, it's very abstract that the speed, ...
3
votes
1answer
164 views

What does the appearance of a classical particle fundamentally reduce to?

I've been reading an article that describes what seems to be a classical particle as a regularity in the global wavefunction over a quantum configuration space: When you actually see an electron ...
3
votes
2answers
538 views

Is the free electron wavefunction stable?

The wavefunction of a free electrons is variously described as a plane wave or a wave packet. I am fairly happy with the wave packet, as it is localised. But if we change to the electron's rest ...
2
votes
0answers
208 views

Analytic form of the normalization constant for Laughlin wavefunction

Is there any analytic form of the normalization constant for Laughlin wavefunction $$\prod_{i < j} (z_i-z_j)^{1/\nu} e^{-\sum_i |z_i|^2/4}$$ where $\nu$ is the filling factor?
6
votes
3answers
908 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 ...
3
votes
2answers
378 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 ...
2
votes
4answers
234 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 ...
5
votes
3answers
217 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 = ...
2
votes
2answers
919 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 ...
1
vote
1answer
432 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 ...
2
votes
1answer
570 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 ...
1
vote
3answers
545 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} ...
0
votes
1answer
89 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 ...
1
vote
2answers
216 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}} ...
1
vote
1answer
1k 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 ...
3
votes
3answers
768 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 ...
2
votes
1answer
1k 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 ...
0
votes
3answers
457 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 ...
3
votes
1answer
184 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 ...
0
votes
1answer
469 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?
4
votes
1answer
241 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 ...
2
votes
1answer
536 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 ...
2
votes
1answer
445 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 $A(\theta, \phi)$ ...
2
votes
0answers
113 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 ...
4
votes
2answers
358 views

Exactly how is the constant measured velocity of light deduced from Maxwell's equation?

For electromagnetic radiation the velocity of propagation is $c = 1/\sqrt{\mu_0 \epsilon_0}$. Since both $\mu_0$ and $\epsilon_0$ do not vary in any inertial frame, then $c$ must be constant in any ...
1
vote
1answer
331 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
votes
1answer
261 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 ...
0
votes
2answers
609 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 ...
1
vote
2answers
285 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 ...
1
vote
1answer
424 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 ...
0
votes
1answer
241 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 ...
0
votes
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 ...