# Questions tagged [wavefunction]

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. DO NOT USE THIS TAG for classical waves.

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### Which position and momentum distributions arise from some wave function?

Consider a particle in one dimension with wave function $\psi$. The probability density function describing how likely it is to find it in a given position is given by $f(x)=\left|\psi(x)\right|^2$. ...
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### Does the Schrodinger Equation yield a unique wave function and density?

I am learning DFT and the Hohenberg Kohn Theorem of Existence. And it says that there is a one-to-one correspondence between the external potential and the density. However the proofs that I have seen ...
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### Projection operator (relative angular momentum) in FQHE Toy hamiltonian

I am working on Fractional Quantum Hall Effect and reading these lecture notes http://www.damtp.cam.ac.uk/user/tong/qhe/qhe.pdf. As all others sources I have found, none of them precisely define the ...
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### Connection between quantum field and the wavefunction

The general question "What is a quantum field?" has been asked here before, but I'm looking for specific help in trying to iron out the details of my own personal interpretation and understanding. In ...
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### Spherical symmetry of Cooper pair wave function

Can someone please explain to me how the wave function of a Cooper pair is spherically symmetric?
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### The ground state of arbitrary Potential Function

How can one say that the number of nodes in the ground state must be nodeless . And how one can ensure that, when one gets up in the energy spectrum, for consecutive States the difference of number of ...
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### Irreducible representation of derivatives of diabatic electronic wave functions

My question regards the symmetry properties of the derivatives of diabatic electronic wavefunctions. I think the question goes somewhat beyond the standard group theoretical machinery taught in ...
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### Intuitive understanding in QFT

I recently read a bit about the Schrodinger picture in QFT and wavefunctionals, see e.g. Polchinski's String Theory lectures, and I wanted to ask if the intuitive understanding of QFT I got is "right"...
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### Large-scale rotational invariance in lattice space

It is often claimed among physicists that rotational invariance can emerge at large scales in lattice space. Let's focus on quantum mechanics for now. I interpret this claim as follows (I am a ...
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### Is there any utility in conceptualizing a 1D wavefunction as a space-curve?

I was watching animations of different wavefunctions that occur in physics, and it annoyed me that the real and imaginary parts are often graphed on the same axis separately. I wanted to know whether ...
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### Who knows experiments on wave packets spread?

I'm looking for some experimental evidence of quantum wave packets spread to propose to my students. I notice that a huge attention is devoted in books to the theoretical frame, while almost nothing ...
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### Why does a system being in an $s$-wave mean that the spatial wavefunction is symmetric? Does it?

Probably being silly here, but me and my fellow undergrads can't seem to come up with an exact answer to why, if a system is in an $s$-wave, edit: or any orbital with an even value of $\ell$, the ...
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### Is there an intuitive interpretation of the shape of the angular momentum eigenstate?

I was watching a MIT lecture video on angular momentum eigenstate. Toward the end of the lecture, the professor had shown some plots of the first few spherical harmonics, in an attempt to explain ...
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### Nuclear cusp condition

Does the nuclear cusp condition $$\frac{\partial}{\partial r_\alpha} \bar{\rho}(r_\alpha) \vert_{r_\alpha = 0} = -2 Z_\alpha \bar{\rho}(0)$$ hold only for the ground state of a quantum mechanical ...
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### Probability Waves vs. Amplitude Waves

It is often asserted, and it is common knowledge, that the waves associated with a particle are probability waves. This seems reasonable. But what about $E=hf$? This does not seem to be about ...
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### Probability distribution function of the photon's scattering angle

What is the normalized probability distribution function of the photon's scattering angle, $\theta$, in Compton scattering effect when a photon hits an electron?