# 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.

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### What does the general solution of the Schrodinger equation represent for the particle in a box problem?

For the particle in an infinitely deep potential well, I have an intuitive picture of the separable solutions of the Schrodinger equation as being the wavefunctions for the different allowed energy ...
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### Schrödinger operator with a potential defined implicitly

let be the problem $$-\frac{d^{2}}{dx^{2}}y(x)+f(x)y(x)=E_{n}y(x)$$ however we have a problem, we do not know the potential but its inverse $$f^{-1}(x)=g(x)$$ we know $g(x)$ but not $f(x)$ ...
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### Meaning of instantaneous probability densities in time dependent wavefunctions

For a time dependent wavefunction, are the instantaneous probability densities meaningful? (The question applies for instances or more generally short lengths of time that are not multiples of the ...
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### Why minibands are formed in superlattices?

In a single, finite quantum well, there are energy levels defined by the eigenstates - the solutions of the Schroedinger's Equation. The corresponding wavefunctions leak to the barrier because of its ...
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### Schrödinger's equation, time reversal, negative energy and antimatter

You know how there are no antiparticles for the Schrödinger equation, I've been pushing around the equation and have found a solution that seems to indicate there are - I've probably missed something ...
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### 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 ...
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### 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 ...
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### Barrier in an infinite double well

I am stuck on a QM homework problem. The setup is this: (To be clear, the potential in the left and rightmost regions is $0$ while the potential in the center region is $V_0$, and the wavefunction ...
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### Schrödinger equation with complex potential

In 1 dimension what is the solution of the Schrödinger equation with potential $$V(x) = V_r + i V_i$$ Potentials are constant.
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### Why is amplitude of a wavefunction to propagate from $q$ to $q'$ governed by $e^{-\frac{i}{\hbar}HT}$ unitary operator?

In the textbook Quantum Field Theory by A. Zee, it says: In quantum mechanics, the amplitude to propagate from a point $q_i$ to a point $q_f$ in time $T$ is governed by the unitary operator ...
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### What math is needed to understand the Schrödinger equation?

If I now see the Schrödinger equation, I just see a bunch of weird symbols, but I want to know what it actually means. So I'm taking a course of Linear Algebra and I'm planning on starting with PDE's ...
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### How to write Schrodinger equation when a particle with some spin quantity and orbital angular momentum

Quantum mechanics: Suppose that there is a particle with orbital angular momentum $|L|$. But the particle also has spin quantity $|S|$. The question is, how do I reflect this into Schrodinger ...
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### 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 ...
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### Complete set and Klein-Gordon equation

In http://www.physics.ucdavis.edu/~cheng/teaching/230A-s07/rqm2_rev.pdf, it says that when there is some external potential, the Klein-Gordon equation is altered, and it says the following: The ...
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### Electron Incident On A Finite Potential Barrier

This is problem 2.8.3 from Miller's Quantum Mechanics For Scientists And Engineers. I'm getting stuck when I try to figure out the wave equation on the right-hand side of the barrier. The original ...
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### Explanation of equation that shows a failed approach to relativize Schrodinger equation

I'm reading the Wikipedia page for the Dirac equation: $\rho=\phi^*\phi\,$ ...... $J = -\frac{i\hbar}{2m}(\phi^*\nabla\phi - \phi\nabla\phi^*)$ with the conservation of probability ...
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### How to obtain Dirac equation from Schrodinger equation and special relativity?

I'm reading the Wikipedia page for the Dirac equation: The Dirac equation is superficially similar to the Schrödinger equation for a free massive particle: A) ...
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### a positive potential as $x \rightarrow \infty$

let us suppose i can calculate the asymptotic of any potential $V(x)$ in one dimension , and that i manage to prove that $V(x) \ge 0$ as $x \rightarrow \infty$ could i conclude taht if or big ...
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### 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?
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### Can we have discontinuous wavefunctions in the Infinite Square well?

The energy eigenstates of the infinite square well problem look like the Fourier basis of L2 on the interval of the well. So then we should be able to for example make square waves that are an ...
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### Finding $\psi(x,t)$ for a free particle starting from a Gaussian wave profile $\psi(x)$

Consider a free-particle with a Gaussian wavefunction, $$\psi(x)~=~\left(\frac{a}{\pi}\right)^{1/4}e^{-\frac12a x^2},$$ find $\psi(x,t)$. The wavefunction is already normalized, so the next thing to ...
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### 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?
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### Which Schrodinger equation is correct?

In the coordinate representation, in 1D, the wave function depends on space and time, $\Psi(x,t)$, accordingly the time dependent Schrodinger equation is H\Psi(x,t) = ...
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