# Questions tagged [spherical-harmonics]

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### EM Field Quantization in Spherical polars

Is it possible to quantize the electromagnetic field in spherical polar coordinates instead of cartesian ones? Such that creation and annihilation operators correspond to harmonic oscillator modes ...
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### In General Relativity, can I represent a Tetrad/Frame field in terms of ladder operators?

I've been interested in expressing the metric tensor $g$ in terms of it's harmonic expansions. In particular I'm interested in writing the tetrad/frame-fields in terms of such expansions. For ...
38 views

### Do relativistically-contracted electron states have the same energy and angular momentum values?

I've been reading that electron bound states are defined by four quantum numbers, $n$, $l$, $m_l$, and $m_s$, respectively the principal quantum number, the azimuthal quantum number, the magnetic ...
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### conducting hollow sphere in magnetic monopole

if a hollow copper sphere(or any conducting hollow sphere) is connected to dc at points diametrical and a magnetic monopole is right at the center of the sphere then will there be any movement of the ...
129 views

### Rewriting $\langle {\bf k} \vert E,l,m \rangle$ as $\langle {\bf k} \vert ~k,l,m \rangle$ Spherical Harmonics

From Sakurai eq. 6.4.21a we have that $$\langle {\bf k} \vert E,l,m \rangle=\frac{\hbar}{\sqrt{M k}}\delta\left(E-\frac{\hbar^2 k^2 }{2M}\right) Y_l^m({\bf\hat k}),$$ where $M$ is the mass of the ...
564 views

### Total angular momentum in multielectron atoms

I have some confusion about orbitals in multielectron atoms. Let's say we consider an atom (Lithium, for example, $1s^2\, 2p^1$) and that the state of the last electron is [n=2, l=1, ml=0, s=1/2, ms=...
47 views

Introduction A planetary magnetic field $\vec{B}$ can be described outside of the planet using Gauss coefficients $g_n^m$ and $h_n^m$ and a spherical harmonic expansion: $$\vec{B} \;=\; -\vec{\... 0answers 45 views ### Hydrogen Atom, polar equation eigenfunctions In my textbook, Quantum Mechanics by David McIntyre on page 235, the solutions to the polar equation resulting from the separation of variables to the hydrogen atom are the eigenstates: The book ... 0answers 47 views ### What is a force multipole? In a recent talk about physics and mechanics inside the cell, I heard such terms as 'force monopole' and 'force dipole'. What do such terms mean? Are they talking about the angular distributions, ... 2answers 578 views ### Multipole expansion of the electromagnetic field In Jackson's Classical Electrodynamics, section 9.7, he develops the multipole expansion of the electromagnetic fields in terms of the vector spherical harmonics and the spherical Bessel and Hankel ... 0answers 123 views ### How to find an action of (\hat {\sigma} \cdot \hat {\mathbf L} ) on spherical spinors? Let's have the spherical spinors \psi_{j, m, l = j \pm \frac{1}{2}},$$ Y_{j, m, l = j \pm \frac{1}{2}} = \frac{1}{\sqrt{2l + 1}}\begin{pmatrix} \pm \sqrt{l \pm m +\frac{1}{2}}Y_{l, m - \frac{1}{2}} ...
Question: A hydrogen atom is located in a quadrupole field, which gives it a perturbation $$H_1=A(x^2-y^2)$$ where $A$ is some constant. Calculate the quantity \$...