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

2
votes
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 ...
2
votes
1answer
80 views

Inconsistency in the delta potential

I encountered an inconsistency in the one-dimensional delta potential. Suppose we have a one-dimensional infinitely deep square well from $-L$ to $+L$. We know the eigenstates are sine and cosine ...
2
votes
2answers
91 views

Wavefunction of isomers

In quantum chemistry, the wavefunction for a molecule can be viewed as the output of a function $\xi(m, n_1,..., n_k)$ with $m, n_i \in \mathbb{Z}^+$ that returns a $|\psi\rangle$ that satisfies a ...
2
votes
3answers
72 views

Koopmann von Neumann (KvN) Theory

I was just wondering does anyone have any informative sources apart from the obvious wikipedia articles regarding Koopmann von Neumann (KvN) theory? Or if its possible could someone explain the basic ...
2
votes
1answer
67 views

Eigenfunctions corresponding to degenerate spectra

It is well knwon that an eigenstate can be obtained by superposing wavepackets. In other words, if $\Psi({\bf x},t)$ is the solution of the time dependent Schroedinger equation for an initial ...
2
votes
1answer
106 views

On use of Hamiltonians for Helium

The Hamiltonian of helium can be expressed as the sum of two hydrogen Hamiltonians and that of the Coulomb interaction of two electrons. $$\hat H = \hat H_1 + \hat H_2 + \hat H_{1,2}.$$ The wave ...
2
votes
1answer
130 views

Kronig-Penney model

I am studying the Kronig-Penney model as treated in the book by Kittel: Introduction to Solid State Physics. In this model one considers a period potential which is zero in the region $[0,a]$ ...
2
votes
1answer
108 views

Expectation value of Hamiltonian in different pictures of quantum mechanics

We start with the familiar Schrodinger equation: $$ i\hbar \frac{\partial \left|\psi_S\right\rangle}{\partial t} = \hat{H}_S \left|\psi_S\right\rangle $$ As we switch to a different picture than ...
2
votes
2answers
61 views

How do I describe two entangled electrons in the same state except for a different spin

I am trying to formulate the wave function that describes two entangled electons having the same position but opposite spin. According to the Pauli exclusion principle this should be possible. And ...
2
votes
2answers
148 views

Box normalisation and Particle in a box - Quantum Mechanics

I have been long itched by this issue of subtle difference between box-normalised free particle and infinite-dimensional potential well. Choosing a one dimensional case, the Hamiltonian in two cases ...
2
votes
2answers
124 views

Infinite well particle subject to additional time dep. potential

I am asked to find the wavefunction of the particle in a well subject to an additional potential $$V(x,t)=\frac{\pi x \hbar}{L}\delta(t).$$ I have already solved that ...
2
votes
2answers
239 views

Wave function for an electron in and around a small charged sphere

I am interested in solutions of the Schroedinger equation. For simplicity I started my studies with the $n=1$ ground state of the hydrogen atom. I was particularly interested in the higher moments of ...
2
votes
1answer
153 views

Possible Outcomes from Measuring a Hydrogen Atom

A hydrogen atom is characterized by the wavefunction $$\mid \psi \rangle =\sqrt{\frac{2}{7}}\mid 4\,2\,1\rangle +\sqrt{\frac{1}{7}}\mid 2 \,1\,\bar{1}\rangle+\sqrt{\frac{4}{7}}\mid 3\,2\,0\rangle$$ ...
2
votes
1answer
274 views

Probability current vs. direction of wave function

I did an exercise for my Quantum-Mechanics Lecture: Let $\hbar$=2m=1. A particle in 1 dimension has $j(x)=2\ Im(\overline{\psi} (x) \ \psi'(x))$ and it's to show that there are superpositions $\psi ...
2
votes
1answer
307 views

Given wave function at $t=0$, what is the process of deriving time dependent wave equation? [closed]

Suppose $$\Psi (x, t=0)=Ae^{i\alpha _1}\psi _1(x)+Be^{i\alpha _2}\psi_2(x)+Ce^{i\alpha _3}\psi_3(x).$$ If $\psi _n$ are the energy eigenfunctions how would I derive $\Psi (x,t)$? I am having trouble ...
2
votes
3answers
146 views

Non-normalizable QM bound state in 4 spatial dimensions?

Edit 26/Sept/13: Fixed Typo in potential I'm solving the following (seemingly simple) quantum-mechanical problem in four spatial dimensions. In natural units ($\hbar^2/2m=1$), the Schrödinger ...
2
votes
3answers
254 views

Implicit Postulate of Quantum Mechanics

Consider the following quantum system: a particle in a one dimensional box (= infinite potential well). The energy eigenstates wave functions all vanish outside the box. But the position eigenstates ...
2
votes
2answers
258 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
1answer
232 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
2answers
206 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
1answer
657 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 ...
2
votes
0answers
32 views

Wave/particle-duality as result of taking different limits of a QFT

There is an account on dualities in quantum field theories and string theories by Polchinski from last week http://arxiv.org/abs/1412.5704 At the end of page 4, he writes the wave/particle ...
2
votes
0answers
48 views

Estimate of the second shallowest bound state?

Suppose we have a 1D potential $V(x)$ of finite range, i.e., $$ V(x) ~=~0 $$ for $|x| > b $. The potential is assume to support at least two bound states, but might have more, say $n\geq 2$. ...
2
votes
1answer
124 views

Normalization of a wavefunction that's superposition of two unknown energy eigenfunctions

Question:$$\psi(x)=A(3u_1(x)+4u_2(x))$$where $u_1(x)$ and $u_2(x)$ are energy eigenfunctions. How to normalize function $\psi(x)$? My intuitive solution: I got ...
2
votes
0answers
29 views

How does a photon travel through an electron cloud?

We all know that the exact position and exact velocity of an electron in an atom cannot be determined simultaneously, as per the Heisenberg uncertainty principle. We only talk about the probability of ...
2
votes
0answers
39 views

Relation between p+ip wave Superconductor and Moore-Read State

I am quite interested in the understanding of the relation between p_ip wave superconductor(SC) and the Moore-Read(MR) state. They share many similar properties, for example, p+ip SC has majorana as ...
2
votes
2answers
57 views

How will a particle with energy less than $V_{\rm min}$ behave?

Consider e.g. the finite square well: $V = -V_o$ between $x=-a$ and $x=a$, $V=0$ elsewhere Now for scattering states, $E$ must be $> 0$. For normalizable bound states, $E$ must be $< 0$ and ...
2
votes
1answer
100 views

Electron distribution around atom when moving

I do not have much experience on this but if an atom has some electrons around nucleus and the atom itself it is moving at some speed does that affect the distribution of electrons around? I am ...
2
votes
0answers
94 views

Momentum representation of a state

I am trying to figure out the momentum representation of the state which has the properties $$\langle \psi |\hat q |\psi \rangle=-q_0,$$ $$\langle\psi|\hat p|\psi \rangle=p_0, $$$$\Delta q\Delta ...
2
votes
0answers
208 views

Double slit experiment and entanglement

Just wondering, what would happen in this experiment. In the experiment you would first have two entangled particles. Then you fire one of the particles, lets say "Particle A", at a double slit ...
2
votes
0answers
37 views

Rydberg quasimolecules & stark states?

I found this image : on the internet and I traced it back to this article ,I wanted to use it as part of an architectural visualization for my project(architecture) but for this to happen I need to ...
2
votes
0answers
105 views

A general wavefunction in a square lattice

Suppose we have a square lattice with periodic condition in both $x$ and $y$ direction with four atoms per unit cell, the configuration of the four atoms has $C_4$ symmetry. What will be a general ...
2
votes
0answers
276 views

Probability and probability amplitude [duplicate]

What made scientists believe that we should calculate probability $P$ as the $P = \left|\psi\right|^2$ in quantum mechanics? Was it the double slit experiment? How? Is there anywhere in the ...
2
votes
1answer
92 views

What does $\psi_j(r_i)$ mean?

I have a mean-field Hamiltonian for N electrons. The mean-field potential felt by electron $i$ at position ${\bf r}_i$ is given by $V^{(i)}_{int}({\bf r}_i)=\sum_{j\ne i}|\psi_j({\bf r}_i)|^2$ I ...
2
votes
0answers
239 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?
2
votes
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 ...
1
vote
2answers
255 views

How to know if a wave function is physically acceptable solution of a Schrödinger equation?

How does one decide whether a wave function is a physically acceptable solution of the Schrödinger equation? For example: $\tan x$ , $\sin x$, $1/x$, and so on.
1
vote
4answers
269 views

Having trouble understanding some stuff about delta functions [closed]

I was going through one of the examples in Griffith's Quantum book and there was a few things in Example 3.3 that I didn't understand that I was hoping to get some clarification on. For instance, we ...
1
vote
1answer
284 views

Quantum harmonic Oscillator analytic method

I'm using a book from Griffiths, I got really stuck about how he arrived at the approximate solution, is it just by trying( trial solution method?), I really appreciate any help on this. ...
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, ...
1
vote
2answers
257 views

Hilbert space and Hamiltonians

Assume a system described by a Hamiltonian H, and assume that the eigenstates of H, $φ_i$(r) are integrable in absolute square. We say that these states belong to a Hilbert space (they can even form a ...
1
vote
3answers
287 views

Interpretation of the wave function in quantum mechanics

I just started watching the coursera lectures on the basics of quantum mechanics and one of the first lectures were on deriving Schrodinger's equation and its interpretation it under Born's ...
1
vote
1answer
560 views

Solution of 1-D Schrodinger equation for the potential $V(x) = -\frac{1}{|x|}$

May be this question might have already been asked but i couldn't find it, so let me know if its already there. Consider a potential, $V(x) = -\frac{1}{|x|}$ and if we apply this to a one dimensional ...
1
vote
2answers
88 views

How would you go about evaluating $\langle \psi \mid 100 \mid \psi \rangle$? [closed]

How would you go about evaluating $\langle \psi \mid 100 \mid \psi \rangle$? I just can't seem to figure this out, and I know it isn't hard.
1
vote
3answers
107 views

Variational Theorem proof

I have been trying to prove variational theorem in quantum mechanics for a couple of days but I can't understand the logic behind certain steps. Here is what I have so far: \begin{equation} ...
1
vote
2answers
168 views

Determining the Wave Function From Initial Conditions

This is Problem 2.6 (b) in Griffiths, Intro to QM: A particle in an infinite square well has its initial wave function an even mixture of the first two stationary states: $\Psi(x,0) = ...
1
vote
2answers
279 views

General wavefunction and Schrödinger Equation

I'm starting with quantum mechanics and the book I follow (Griffiths) first introduces the wavefunction as the probability density of the position of a 0-spin single particle. Later on I've realized ...
1
vote
2answers
2k views

The Energy Eigenvalue of a Wavefunction

I've been reading an introduction to quantum mechanics online, and while constructing the Schrodinger equation for a free particle, the equation $i\hbar \frac{d \Psi}{dt}=\hbar\omega\Psi$ is obtained. ...
1
vote
1answer
467 views

Mathematical explanation of quantum teleportation

I am now studying quantum teleportation. I get what the process is like but I'm wondering why it happens this way. You've got two entangled particles A and B whose wavefunctions are entangled. You ...
1
vote
1answer
2k views

Plane wave expansion in cylindrical coordinates

I am trying to solve scattering problem in 2D and got to expand the wave function in cylindrical system which comes out to be Hankel function. Can you tell me how to expand the plane wave $\exp(i ...