# 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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### How to tell if a complex exponential blows up

I'm following Griffiths' Introduction to Quantum Mechanics, where he's discussing the general solution to the delta-function potential problem. The solution he refers to is ...
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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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### Tunneling and transmission

Lets say we have a tunelling problem in the picture, where $W_p$ is a finite potential step: If particle is comming from the left a general solutions to the Schrödinger equations for sepparate ...
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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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### Many-worlds: how often is the split how many are the universes? (And how do you model this mathematically.)

When I read descriptions of the many-worlds interpretation of quantum mechanics, they say things like "every possible outcome of every event defines or exists in its own history or world", but is this ...
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### The eigenvalue of Schrodinger Equation

I'm a student majoring in Mathematics.But now I'm studying the KDV equation which uses Schrodinger Equation. My question is that in time-independent Schrodinger ...
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### Projection of states after measurement

Continuing from the my previous 2-state system problem, I am told that the observable corresponding to the linear operator $\hat{L}$ is measured and we get the +1 state. Then it asks for the ...
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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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### Can we solve the particle in an infinite well in QM using creation and annihilation operators?

The particle in an infinite potential well in QM is usually solved by easily solving Schrodinger differential equation. On the other hand particle in the harmonic oscillator oscillator potential can ...
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### Change of basis in non-linear Schrodinger equation

At the mean-field level, the dynamics of a polariton condensate can be described by a type of nonlinear Schrodinger equation (Gross-Pitaevskii-type), for a classical (complex-number) wavefunction ...
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### Plotting $\psi$ for finite square well potential

Lets say we have a finite square potential well like below: This well has a $\psi$ which we can combine with $\psi_I$, $\psi_{II}$ and $\psi_{III}$. I have been playing around and got expressions ...
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### How do I determine the location of a free particle with Schrödinger's equation?

I'm trying to get to grips with the Schrödinger equation by looking at a free particle. I'm certain at some point I massively misunderstood something. According to a textbook and a lecture the free ...
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### Is this interpretation of $\psi=\frac{1}{\sqrt{\pi a^{3}}}e^{-r/a}$ correct?

Apologies if this is stating the obvious, but I'm a non-physicist trying to understand Griffiths' discussion of the hydrogen atom in chapter 4 of Introduction to Quantum Mechanics. The wave equation ...
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### Sinusoidal vs exponential wave functions with Schrodinger's equation

When solving Schrodinger's equation, we end up with the following differential equation: $$\frac{{d}^{2}\psi}{dx^2} = -\frac{2m(E - V)}{\hbar}\psi$$ As I understand it, the next step is to guess the ...
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