# Tagged Questions

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### Energy of an Electron in a One Dimensional Periodic Potential

First, we consider the time independent Schrodinger equation of the form: $$\bigg(-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}+u(x) \bigg)\phi_A(x)=E_A\phi_A(x)$$ Where $u(x)$ is a potential created by a ...
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### Doubt in a certain equation of a research paper [closed]

In the following research paper (link provided) , I am not able to figure out how do we get the equation (7) . Please help me out. Also , please recommend the necessary pre requisite text to ...
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### Expected value $<\hat{x}>$ of: $\Phi(x,t)=Ne^{-a[(Mx^2/\hbar)+it]}$ is infinite, why?

The problem says: A particle of mass $M$ is described by the wave function: $$\Phi(x,t)=Ne^{-a[(Mx^2/\hbar)+it]}$$ where a is a positive constant. Asked to determine such things as the ...
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### Poles for a particle scattered in a delta potential

I am working on problem a professor gave me to get an idea for the research he does, and have hit a point where I'm having a difficult time seeing where I need to go from where I'm at. I would also ...
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### Divergent solution in time-dependent Schrödinger equation

if I transform the time-dependent Schrödinger equation without a potential I get: $$- \hbar \omega \psi(\omega,x) = \frac{- \hbar^2}{2m} \frac{\partial^2 \psi(\omega,x)}{\partial x^2}$$ The ...
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### Relating Schrödinger's Wave Equation and Heisenberg Uncertainty Principle

A homework question that I don't conceptually understand: A quantum particle of mass M is trapped inside an infinite, one-dimensional square well of width $L$. If we were to solve Schrodinger's wave ...
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### Schrödinger's Equation and the depth of a finite potential well

Before I ask my question, I have to stress: I have absolutely no idea what the math is going on. I've read my textbook, several Wikipedia articles, scoured the internet, and don't feel anymore ...
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### How to solve Schrödinger's equation for this potential algebraically?

I want to solve Schrödinger's equation with the potential $$V(x)=\frac{1}{2}mx^2+\lambda x$$ algebraically? Is there any way to construct ladder operators that are similar to the one for the harmonic ...
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### Wavefunction as a combination of two stationary states - how to find those states?

Lets say we have a particle in a infinite square well which has a wavefunction like this ($A$ is some constant and $d$ is the width of the well): \begin{align} A\left[ \sin \left(\frac{2 \pi ...
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### 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 ...