# Tagged Questions

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.

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### Switching Parity in a Superconductor

I've got a pretty simple question that's been bothering me for a while. This is the issue. Suppose we have a superconductor with phase $\phi$, and we change this to $\phi+2\pi$. One would think that ...
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### Is it possible to reconstruct the Hamiltonian from knowledge of its ground state wave function?

Is it possible to "construct" the Hamiltonian of a system if its ground state wave function (or functional) is known? I understand one should not expect this to be generically true since the ...
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### Quantization of energy in semi-infinite well

Consider an electron with total energy $E>V_2$ in a potential with $$V(x)= \begin{cases} \infty & x< 0 \\ V_1 & 0< x< L \\ V_2 & x>L \end{cases}$$ ...
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### Applicability of wavefunction matching when Hamiltonian (not just potential) varies

A simple tunnelling calculation can be performed for a potential step by calculating the eigenfunctions for the Hamiltonian on either side of the step and matching the wavefunctions (and using ...
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### How can an orbital be recognised from the wavefunction notation?

I am a student and was working up the exercises in my book when I came across a problem that required me to identify the orbital given by $\psi_{3,2,1}\,.$ What I can work out is that the sub-shell ...
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### Protocol for solving time independent Schrodinger equation

Just a short question about the protocol for solving the time-independent Schrodinger equation for different potentials and the reasons for accepting and rejecting solutions. Take for example the ...
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### Gauge transformation of vector potential multiplies wavefunction by phase

Consider an electron in an electromagnetic field with scalar and vector potentials $\phi, \mathbf{A}$. Suppose for simplicity that $\mathbf{A}$ is time independent. Suppose also that we know the ...
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### Can a quantum mechanical system have more than one wave-function?

I was told that a quantum mechanical system is completely determined by its wave function. But superposition principle says that given two wave functions of some system, a linear combination of them ...
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### Why does a electric Potential have to be real, but not a Potential in quantum mechanics?

So I had this Problem when I had to learn about classical electromagnetism: Why is it, that we use complex numbers when calculating stuff, but in the end only the real part is important (for example ...
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### Can a physical wavefunction be non-smooth (its first derivative is discontinuous)?

Here's an argument that might support the statement that such a non-smooth wavefunction is not physical: You cannot add a finite number of smooth functions to get a non-smooth function. By fourier ...
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### Energy Conservation in Changing Potential Well

If you prepare a particle in a basis state, $|n\rangle$ of an infinite potential well of length $L$, the energy of that state will be $\langle E\rangle = E_n$, with zero variance. If you then ...
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### How can we justify identifying the Dirac delta function with the eigenfunction of position? [duplicate]

I can think of at least two different ways to understand eigenfunctions of operators in quantum mechanics. But neither one seems to provide a good explanation for why we take the position-basis ...
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### Is there one wavefunction per field? [closed]

Is the big picture of quantum field theory that: There are fields (EM, electron, Higgs, gravity, etc.) A field can be described by a wavefunction indicating the probability density of 1 or more '...
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### Mathematical definition of wavefront in case of non harmonic waves

What is the general mathematical definition of wavefront? Wavefront is the surface where, at fixed time, the phase is constant But for non-harmonic waves we cannot talk about phase as the ...
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### What happens when two wavefunctions meet?

Apologies for the over-broad question(s), but I'm having a hard time finding out where to look to answer these myself: If a particle is a wavefunction describing a probability amplitude distributed ...