# 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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### 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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### 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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### 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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### 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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### 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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### Orthogonalizing a Gaussian Basis

Given a discrete Gaussian basis $$G = \{\lvert n\rangle, n \in \mathbb{Z}\},$$ where $$\langle x\rvert n \rangle = \exp\left(\dfrac{-(x-nL)^2}{2}\right),$$ with $L$ fixed. Does there exist a set of ...
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### How to evaluate the probability when a particle is detected?

Everyone knows the standard probability interpretation of the quantum mechanics. For example, the wave function of some particle at some time $t$ is $\psi (x,t)$. Therefore, if the particle is ...
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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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### Normalized probability distribution from the Coulomb/Rutherford scattering amplitude?

My question appears elementary, but I have been pretty vexed trying to answer it precisely. Can one use the Rutherford/Coulomb scattering amplitude to get a finite, normalized momentum-space ...
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### Envelope of wavepacket and group velocity

In this answer a possible derivation of the group velocity is provided. It is, anyway, based on the assumption that there will always be a point where all the cosines will sum with the same phase: ...
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### Wave packets in Dirac equation

Gaussian wave packets remain Gaussians after evolution in case of the Schrodinger equation. It is a very useful property of these wave packets. I don't think the same is true for a Gaussian wave ...
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### Analytic form of the normalization constant for Laughlin wavefunction

Is there any analytic form of the normalization constant for Laughlin wavefunction $$\prod_{i < j} (z_i-z_j)^{1/\nu} e^{-\sum_i |z_i|^2/4}$$ where $\nu$ is the filling factor?
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### Where in experiment do you encounter Lorentizan wavefunction?

Is there an experimental system, or such that can be observed in nature where a particle's wave function assumes a form - $\psi(x)\propto \frac{1}{\sqrt{x^2+1}}$ such that $|\psi(x)|^2$ is Lorentzian? ...
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### Is there any dependence between the shape and dynamics of the electric field produced by an electron and 'shape' of its wave function?

In classical electromagnetism the electron is described by a point charge that generates an electric field with spherical symmetry when the electron is static but at the quantum level the electron is ...
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### Intuiting qualitatively the shapes of the eigenfunctions of a finite well-like potential, using the infinite well eigenfunctions as an inspiration

Consider, for example, the third excited state of an infinite square well: Now consider the following potential: If we wanted to sketch the rough shape of the third excited eigenfunction of this ...
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### Wave function as a section of a complex line bundle to do QM in polar coordinates

If you want to change the coordinates of a Wave function $\Psi$ in 2D QM from cartesian to polar coordinates in a naive way one encounters a problem, namely the (naively defined) radial momentum ...
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### Symmetric potential well different solutions

I have solved $H|\psi\rangle=E_{n}|\psi\rangle$ with $V(x)=0$ from $-a<x<a$ and $\infty$ otherwise. If I propose a solution of the form $\psi(x)=A_{n}e^{ikx}+B_{n}e^{-ikx}$ I arrive to the ...
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### Can one add a discrete set of functions to complete the bound states of the hydrogen atom?

Though being an infinite orthonormal set of functions, the bound states $\Psi_{nlm}$ of the hydrogen atom do not form a basis of the Hilbert space $L^2(\mathbb{R}^3)$ due to the continuous spectrum, i....
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