# Tagged Questions

Partial differential equation which describes the time evolution of the wavefunction of a quantum system. It is one of the first and most fundamental equations of quantum mechanics.

4answers
756 views

### In quantum mechanics, given certain energy spectrum can one generate the corresponding potential?

A typical problem in quantum mechanics is to calculate the spectrum that corresponds to a given potential. Is there a one to one correspondence between the potential and its spectrum? If the ...
6answers
946 views

### Why can we treat quantum scattering problems as time-independent?

From what I remember in my undergraduate quantum mechanics class, we treated scattering of non-relativistic particles from a static potential like this: Solve the time-independent Schrodinger ...
1answer
1k views

### Schrödinger Equation

I am reading up on the Schrödinger equation and I quote Because the potential is symmetric under $x\to-x$, we expect that there will be solutions of definite parity. Could someone kindly explain ...
2answers
681 views

### Schrodinger equation in spherical coordinates

I read a paper on solving Schrodinger equation with central potential, and I wonder how the author get the equation(2) below. Full text. In Griffiths's book, it reads ...
2answers
1k views

### Is the Schrödinger equation derived or postulated?

I'm an undergraduate mathematics student trying to understand some quantum mechanics, but I'm having a hard time understanding what is the status of the Schrödinger equation. In some places I've read ...
3answers
660 views

### Schrodinger's equation (explanation to non physicist)

For a report I'm writing on Quantum Computing, I'm interested in understanding a little about this famous equation. I'm an undergraduate student of math, so I can bear some formalism in the ...
5answers
824 views

### The Many Body problem

(This is a simple question, with likely a rather involved answer.) What are the primary obstacles to solve the many-body problem in quantum mechanics? Specifically, if we have a Hamiltonian for a ...
4answers
466 views

### Quantum mechanics as classical field theory

Can we view the normal, non-relativistic quantum mechanics as a classical fields? I know, that one can derive the Schrödinger equation from the Lagrangian density {\cal L} ~=~ \frac{i\hbar}{2} ...
1answer
381 views

### Interpretation of the Random Schrödinger Equation

I should preface this by admitting that my physics background is rather weak so I beg you to keep that in mind in your responses. I work in mathematics (specifically probability theory) and a paper ...
2answers
391 views

### Solving the Schrödinger equation for the double-slit experiment

I'm not sure if this is the right place to ask a question about the Schrödinger equation, but I'll take my chances anyway. Basically, I would like to know how one can set up a potential function that ...
1answer
1k views

### Eigenfunctions v.s. eigenstates

Is there a difference between "eigenfunction" and "eigenstate"? They seem to be used interchangeably in texts, which is confusing. My guess is that an "eigenfunction" has an explicit ...
2answers
444 views

### Why does iteratively solving the Hartree-Fock equations result in convergence?

[ Cross-posted to the Computational Science Stack Exchange: http://scicomp.stackexchange.com/questions/1297/why-does-iteratively-solving-the-hartree-fock-equations-result-in-convergence ] In the ...
0answers
217 views

### exponential potential $\exp(|x|)$

For $a$ being positive what are the quantization conditions for an exponential potential? $$- \frac{d^{2}}{dx^{2}}y(x)+ ae^{|x|}y(x)=E_{n}y(x)$$ with boundary conditions $$y(0)=0=y(\infty)$$ I ...
4answers
278 views

### Examples of exact many-body ground state wavefunction

Is there any non-trivial many-body system for which the exact solution to Schrödinger's equation is known? (By non-trivial, I mean a system with particle-particle interactions.) Perhaps something like ...
2answers
781 views

### Matrix Representations of Quantum States and Hamiltonians

I am a high school student trying to teach himself quantum mechanics just for fun, and I am a bit confused. As a fun test of my programming/quantum mechanics skill, I decided to create a computer ...
1answer
196 views

### Nomenclature of radial solutions to the Schrodinger Equation

For the free particle with quantum number $l=0$, the regular solution to the radial Schrodinger equation is $R_0 (\rho)=\frac{\sin{\rho}}{\rho}$ while the irregular solution is \$R_0 ...
3answers
250 views

### Rationale for writing wave function as product of independent wave functions

When solving Schrödinger's equation for a 3D quantum well with infinite barriers, my reference states that: \psi(x,y,z) = \psi(x)\psi(y)\psi(z) \quad\text{when}\quad V(x,y,z) = V(x) + V(y) + V(z) = ...
5answers
525 views

### Derivation of Schrodinger equation for a system with position dependent effective mass

How to derive the Schrodinger equation for a system with position dependent effective mass? For example, I encountered this equation when I first studied semiconductor hetero-structures. All the books ...
3answers
143 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 = ...
2answers
2k views

### Solving one dimensional Schrodinger equation with finite difference method

Consider the one-dimensional Schrodinger equation $$-\frac{1}{2}D^2 \psi(x)+V(x)\psi(x)=E\psi(x)$$ where $D^2=\dfrac{d^2}{dx^2},V(x)=-\dfrac{1}{|x|}$. I want to calculate the ground state ...
1answer
775 views

### Madelung transformation

What is the Madelung transformation and how is it used?
3answers
463 views

### What is the relationship between Schrödinger equation and Boltzmann equation?

The Schrödinger equation in its variants for many particle systems gives the full time evolution of the system. Likewise, the Boltzmann equation is often the starting point in classical gas dynamics. ...
2answers
125 views

### Is there a time delay during tunnelling?

A particle hitting a square potential barrier can tunnel through it to get to the other side and carry on. Is there a time delay in this process?
1answer
174 views

### What type of PDE are Navier-Stokes equations, and Schrödinger equation?

What type of PDE are Navier-Stokes equations, and Schrödinger equation? I mean, are they parabolic, hyperbolic, elliptic PDEs?
1answer
108 views

### Apparent contradiction between calculations and intuition?

I am rather confused because it would seem that mathematical conclusions I have drawn here goes against my physical intuition, though both aren't too reliable to begin with. We have a potential step ...
3answers
333 views

### Nonlinear dynamics beneath quantum mechanics?

Yesterday I asked whether the Schroedinger Equation could possibly be nonlinear, after reviewing the answers and material given to me in that thread I feel like my question were adequately answered. ...
5answers
739 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 part ...
1answer
107 views

### Temporal part of Quantum Wavefunction

I was hoping that someone could give me the more fundamental reason that we take as the temporal part of a quantum wavefunction the function $e^{-i\omega t}$ and not $e^{+i\omega t}$? Clearly ...
2answers
177 views

### Why must the angular part of the Schrodinger Equation be an eigenfunction of L^2?

I was reading about the solution to the Schrodinger Equation in spherical coordinates with a radially symmetric potential, $V(r)$, and the book split the wavefunction into two parts: an angular part ...
1answer
79 views

### What are relativistic and radiative effects (in quantum simulation)?

I'm reading about Quantum Monte Carlo, and I see that some people are trying to calculate hydrogen and helium energies as accurately as possible. QMC with Green's function or Diffusion QMC seem to be ...
2answers
554 views

### Radial Schrodinger equation with inverse power law potential

Recently I read a paper about solving radial Schrodinger equation with inverse power law potential. Consider the radial Schrodinger equation(simply set $\mu=\hbar=1$): ...
2answers
296 views

### Does String theory say that spacetime is not fundamental but should be considered an emergent phenomenon?

Does String theory say that spacetime is not fundamental but should be considered an emergent phenomenon? If so, can quantum mechanics describe the universe at high energies where there is no ...
2answers
671 views

### On numerically solving the Schrödinger equation

I just read a paper 'A pocket calculator determination of energy eigenvalues' by J Killingbeck (1979). Link: http://iopscience.iop.org/0305-4470/10/6/001 I have some questions about section 2. Why ...
2answers
2k views

### Zero probability of finding an electron in the nucleus

One and the same electron in a p orbital and taking part in a common π (pi) bond has two lobes visualized as connecting through the nucleus. There is however zero probability of finding an electron at ...
2answers
83 views

### Do we always ignore zero energy solutions to the (one dimensional) Schrödinger equation?

When we solve the Schrödinger equation on an infinite domain with a given potential $U$, much of the time the lowest possible energy for a solution corresponds to a non-zero energy. For example, for ...
1answer
193 views

### Gross-Pitaevskii equation in Bose-Einstein condensates

I was hoping someone might be able to give a approachable explanation of the Gross-Pitaevskii equation. All the sources I've been able to find seem to concentrate on the derivation, and I don't have ...
1answer
1k views

### What inspired Schrödinger to derive his equation?

I have almost no background in physics and I had a question related to Schrodinger's Equation. I think, it is not really research level so feel free to close it, but I would request you to kindly ...
2answers
418 views

### Use of Operators in Quantum Mechanics

I understand the form of operators in use for quantum mechanics such as the momentum operator: $$\hat{\text{P}}=-ih\frac{d}{dx}$$ My question is in what ways can I use it and what am I getting back? ...
2answers
326 views

### Quantum Mechanics: Show that the expectation value of angular momentum does not change with time

The potential is given by $V\left(\left\|(x,y,z)\right\|\right)$, so $[\hat{L}, \hat{H}] = 0$. Using the definition of $\langle \hat{L} \rangle$ and the time-dependent Schrödinger equation, show that ...
1answer
251 views

### Is momentum conservation for the classical Schrödinger equation due to non-relativistic or due to some more exotic invariance?

I had no problem appliying the Neothers theorem for translations to the non-relativistic Schrödinger equation \$\mathrm i\hbar\frac{\partial}{\partial t}\psi(\mathbf{r},t) \;=\; \left(- ...
5answers
382 views

### How isolated must a system be for it's wave function to be considered not collapsed?

As an undergrad I was often confused over people's bafflement with Schodinger's cat thought experiment. It seemed obvious to me that the term "observation" referred to the Geiger counter, not the ...
2answers
88 views

### Solve the angular part of Schrodinger equation numerically

I would like to solve the angular part (the one for what is usually called the $\theta$ angle) of a time-independent 3D Schrodinger equation  \frac{\mathrm{d}}{\mathrm{d}x}\left[ (1-x^2) ...
4answers
669 views

### Where is spin in the Schroedinger equation of an electron in the hydrogen atom?

In my current quantum mechanics, course, we have derived in full (I believe?) the wave equations for the time-independent stationary states of the hydrogen atom. We are told that the Pauli Exclusion ...
2answers
446 views

### Infinite square well

1. Given that for an infinite square well problem, $\psi(x,0)=\frac{6}{a^3}x(a-x)$, I can show by Fourier transform that the probability of measuring $E_n$  for $n$ even is 0. But is there a physical ...
2answers
268 views

### Galilean invariance of the Schrodinger equation

I am only asking this question so that I can write an answer myself with the content found here: http://en.wikipedia.org/wiki/User:Likebox/Schrodinger#Galilean_invariance and here: ...
2answers
108 views

### Time-dependence in LCAO

I would like to study time-dependence (TD) in linear combinations of atomic orbitals (LCAO). The Hückel method enables quick and dirty determination of MOs for suitable systems (view link for ...
1answer
128 views

### How does a state in quantum mechanics evolve?

I have a question about the time evolution of a state in quantum mechanics. The time-dependent Schrodinger equation is given as $$i\hbar\frac{d}{dt}|\psi(t)\rangle = H|\psi(t)\rangle$$ I am ...
3answers
339 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 ...
1answer
728 views

### Light waves and Schrödinger probability waves

Ok, bearing in mind that I only have a brief understanding of quantum mechanics (no formal education, only from reading about concepts in books), so I could be way off here, I have a question ...
1answer
134 views

### Schrödinger equation for a harmonic oscillator

I have came across this equation for quantum harmonic oscillator $$W \psi = - \frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2} + \frac{1}{2} m \omega^2 x^2 \psi$$ which is often remodelled by defining a new ...
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