# 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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### Where does $\hat{P}\psi(x) = -i\hbar \partial_x \psi(x)$ come from?

It's a very basic question, where does the relation $$\hat{P}\psi(x) = -i\hbar \partial_x \psi(x)$$ for any square integrable $\psi(x)$ come into existence? Some texts I found states that the above ...
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### Do wave functions really belong to $L^2$ space, or do we need to restrict our physical Hilbert space even further?

I am beginning to study quantum mechanics and I got stuck right at the beginning. I am trying to prove that the time derivative of the expected value of momentum of a particle is the (negative) ...
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### What happens to the wave function of a particle immediately after measuring its energy?

For this question, I will be adhering to the Copenhagen interpretation (since that's what I've learned in university so far). For the sake of brevity/clarity, also, assume the Hamiltonian here has ...
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### Physical reason why the derivative of a wavefunction has to be continuous?

Question What is the physical reason (i.e. without any maths) that the derivative of a wavefunction (except with infinite potentials) has to be continuous? Other info I know that in the classical ...
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### How do you determine the “phase” of a hydrogen eigenfunction?

I've been reading the wikipedia article on the atomic orbitals of hydrogen. They have a nice collection of diagrams, such as this one for n,l,m = 3,1,1 This is apparently showing the wavefunction, ...
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### Quantum Wavefunctions Without Space

A handful of physicists have a rather peculiar definition of 'nothing' in terms of cosmology. Their claim is that the Universe, assuming it has 0 total energy, could have arisen from nothing but ...
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### Why is $\omega = \sqrt{K/m}$ valid for a quantum oscillator?

I'm working in the 3rd edition of Modern Physics by Serway, Moses, and Moyer. In 6.6, it talks about a quantum oscillator. I don't fully understand how the definition of frequency works. Now, we ...
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### Logic of the 'imaginary wave function collapse' argument in Double Slit experiment

My question is in regards to the stance that the 'wave function collapse' is not an actual physical occurrence. That is, you are not, by observation, changing the particles position from a wave to a ...
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### Why do we use $\psi$ instead of a straightforward probability?

What is the advantage/purpose of using $\psi$ for wavefunctions and getting the probability with $|\psi|^2$ as opposed to just defining and using the probability function?
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### At what point is the spin determined in a Stern-Gerlach Apparatus

Consider a particle with spin that travels through a Stern Gerlach box (SGB), which projects the particle’s spin onto one of the eigenstates in the $z$-direction. The SGB defines separate trajectories ...
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### How to find the wavefunction that solves an infinite square well with a delta function well in the middle?

Solutions for the wavefunction in an infinite square well with a delta function barrier in the middle are easily found online (see here for an example). I am wondering what the wavefunction is for an ...
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### Workaround to fermion sign problem?

My (rather incomplete) understanding of the NP-hard fermion/numerical sign problem is that it occurs when attempting to converge on a wavefunction for many-body fermion systems (for example, a small ...
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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 x}{d}\...
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### wavefunction collapse and uncertainty principle

We all know that wavefunction collapse when it is observed. Uncertainty principle states that $\sigma_x \sigma_p \geq \frac {\hbar}{2}$. When wavefunction collapse, doesn't $\sigma_x$ become $0$?, as ...
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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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### Loss of interference in single-photon Mach–Zehnder interferometer with detector in only one arm

I have read that if you have a Mach–Zehnder interferometer (doing a single-photon experiment) and put a non-destructive detector in only one of the two arms (connected to the first beam splitter), you ...