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

3
votes
1answer
679 views

Even and Odd States of a 1D finite potential well

Is it possible for a particle trapped in a 1D finite potential well to evolve from a even state to an odd state and vice-versa? Why?
3
votes
2answers
2k views

How do I figure out the probability of finding a particle between two barriers?

Given a delta function $\alpha\delta(x+a)$ and an infinite energy potential barrier at $[0,\infty)$, calculate the scattered state, calculate the probability of reflection as a function of ...
2
votes
1answer
295 views

Considering the wave function is not 'real', what is interfering?

I find the idea of the wave function being 'just' a collection of numbers (probabilities) quite alluring, and elegant in explaining away the whole 'collapse' business (see Luboš' answer to this ...
1
vote
5answers
3k views

Reason for the Gaussian wave packet spreading

I have recently read how the Gaussian wave packet spreads while propagating. see: http://en.wikipedia.org/wiki/Wave_packet#Gaussian_wavepackets_in_quantum_mechanics Though I understand the ...
5
votes
1answer
300 views

Relativistic contraction for a wave packet and uncertainty on momentum

Consider an electron described by a wave packet of extension $\Delta x$ for experimentalist A in the lab. Now assume experimentalist B is flying at a very high speed with regard to A and observes the ...
2
votes
3answers
14k views

Sinusoidal Wave Displacement Function

I am learning about waves (intro course) and as I was studying Wave Functions, I got a little confused. The book claims that the wave function of a sinusoidal wave moving in the $+x$ direction is ...
2
votes
1answer
267 views

What does the notation $|x_1,x_2\rangle$ mean?

I would like clarification on an equation in the paper "Free matter wave packet teleportation via cold-molecule dynamics", L. Fisch and G. Kurizki, Europhysics Letters 75 (2006), pp. 847-853, DOI: ...
2
votes
2answers
277 views

Wave Function Statistical Interpretation vs Oscillation Interpretation

Can the wave function solution to Schrodinger's Equation be interpreted as an oscillation between all possible measurements (obviously with some type of weighting that would describe the shape of the ...
2
votes
4answers
2k views

Why is wave function so important?

I am almost sure that the wave function is the most important figures in modern physics book. On the other hand I know that wave function even do not have a physical meaning it self alone! Why is ...
8
votes
7answers
808 views

Is it wrong to talk about wave functions of macroscopic bodies?

Does a real macroscopic body, like table, human or a cup permits description as a wave function? When is it possible and when not? For example in the "Statistical Physics, Part I" by Landau & ...
3
votes
1answer
551 views

wavefunction collapse and uncertainty principle

We all know that wavefunction collapse when it is observed. Uncertainty principle states that $\sigma_x \sigma_p \geq \frac {\hbar}{2}$. When wavefunction collapse, doesn't $\sigma_x$ become $0$?, as ...
2
votes
5answers
362 views

wave superposition of electrons and quarks

Is quantum wave superposition of electrons and quarks possible? If not, can different types of elementary particles be mixed in wave superposition?
2
votes
1answer
248 views

How do you determine the degree of localization of a wavefunction?

Suppose that there is a wavefunction $\Psi (x,0)$ where 0 is referring to $t$. Let us also say that $a(k) = \frac{C\alpha}{\sqrt{\pi}}\exp(-\alpha^2k^2)$ is the spectral contents (spectral amplitudes) ...
2
votes
1answer
594 views

How do I solve these integrals of wave function and operator?

First integral $$\int \Psi^*({\bf r},t)\hat {\bf p} \Psi({\bf r},t)\, d^3r,$$ where the $\Psi({\bf r},t)=e^{i({\bf k}\cdot{\bf r}-\omega t)}\,\,\,$ and $\hat {\bf p}=-i\hbar \nabla$. Second one ...
2
votes
2answers
209 views

Measurement and uncertainty principle in QM

The Wikipedia says on the page for the uncertainty principle: Mathematically, the uncertainty relation between position and momentum arises because the expressions of the wave function in the two ...
2
votes
4answers
233 views

Why do we consider the evolution (usually in time) of a wave function?

Why do we consider evolution of a wave function and why is the evolution parameter taken as time, in QM. If we look at a simple wave function $\psi(x,t) = e^{kx - \omega t}$, $x$ is a point in ...
4
votes
1answer
269 views

Why must $\Psi (x,t)$ go to zero faster than $\frac{1}{\sqrt{|x|}}$?

Why must $\Psi (x,t)$ go to zero faster than $\frac{1}{\sqrt{|x|}}$ as $|x|$ goes to $\infty$? According to Griffiths' Introduction to Quantum Mechanics, it must. I don't understand why, and this is ...
0
votes
3answers
3k views

Absolute value sign when normalizing a wave function

I have solved the following problem from Griffiths "Introduction to Quantum Mechanics". Consider the wavefunction: $\Psi (x,t) = A e^{-\lambda |x|} e^{-i\omega t} $ Normalize $\Psi$. Now, we ...
2
votes
2answers
314 views

Why Pauli exclusion instead of electrons canceling out?

To quote Wikipedia, The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions (particles with half-integer spin) may occupy the same quantum state ...
2
votes
1answer
207 views

Why don't cancelling wavefunctions for two different particles give zero total wavefunction?

Let $\left|a\right>=e^{i(kx-\omega t)}$, $\left|b\right>=-e^{i(kx-\omega t)}$ be two neutral particles in the 1D free space without any interaction. Then ...
3
votes
4answers
315 views

Does the wave nature of a particle refer to the wave function?

In quantum mechanics when we talk about the wave nature of particles are we referring in fact to the wave function? Does the wave function describes the probability of finding a particle (ex: ...
3
votes
2answers
636 views

Can we impose a boundary condition on the derivative of the wavefunction through the physical assumptions?

Consider the Schrödinger equation for a particle in one dimension, where we have at least one boundary in the system (say the boundary is at $x=0$ and we are solving for $x>0$). Sometimes we want ...
8
votes
1answer
1k 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
498 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
3k 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
586 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
725 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
456 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
3k 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
775 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 ...
6
votes
5answers
1k views

Hydrogen radial wave function infinity at $r=0$

When trying to solve the Schrödinger equation for hydrogen, one usually splits up the wave function into two parts: $$\psi(r,\phi,\theta)= R(r)Y_{l,m}(\phi,\theta).$$ I understand that the radial ...
1
vote
1answer
501 views

Density of classical states in quantum theory

Let's first treat electrons as classical objects. I can evaluate the classical energy of each state in a configurational space (3N real numbers and, say, spins) using just Coulomb's law. Then I ...
0
votes
1answer
671 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.
4
votes
2answers
785 views

Where does the wave function of the universe live? Please describe its home

Where does the wave function of the universe live? Please describe its home. I think this is the Hilbert space of the universe. (Greater or lesser, depending on which church you belong to.) Or maybe ...
1
vote
3answers
1k 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, ...
4
votes
1answer
203 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
697 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
246 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?
4
votes
1answer
72 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 ...
9
votes
4answers
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 ...
4
votes
2answers
425 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 ...
5
votes
3answers
277 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 = ...
-1
votes
1answer
2k 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?
1
vote
1answer
553 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
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 ...
2
votes
1answer
725 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
690 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} ...
1
vote
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 ...
0
votes
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 ...
1
vote
2answers
232 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}} ...