soft question - Why is the harmonic oscillator so important?
2015年1月13日 · What is the harmonic oscillator? There are at least two fundamental incarnations of "the" harmonic oscillator in physics: the classical harmonic oscillator and the quantum harmonic oscillator. Each of these is a mathematical thing that can be used to model part or all of certain physical systems in either an exact or approximate sense depending ...
A harmoinic oscillator in the Heisenberg picture
2018年8月17日 · Considering the Hamiltonian of a harmonic oscillator \begin{equation} H=\frac{p^2}{2m}+\frac{m\omega^2 x^2}{2}, \end{equation} the time evolution of the Heisenberg picture position and momentum operators is given by \begin{align} \dot{x}&=\frac{i}{\hbar}[H,x]=\frac{p}{m}\\ \dot{p}&=\frac{i}{\hbar}[H,p]=-m\omega^2x, …
quantum mechanics - Heisenberg picture: harmonic oscillator …
2020年3月28日 · I was introduced to the creation and annihilation operators one uses to "intelligently" quantize a harmonic oscillator. I recently heard about the Heisneberg picture, which is apparently similar to the Schrodinger picture but includes time-dependent operators and time-independent wave functions for energy eigenfunctions (i.e. they do not ...
quantum mechanics - Eigenstates of a shifted harmonic oscillator ...
Is it possible to express the eigenstates of this shifted harmonic oscillator with respect to the old eigenstates? It should be possible by using a coherent state I guess, because a coherent state can be seen as kind of a 'shifted' number state.
In what sense is a quantum field an infinite set of harmonic ...
Electromagnetic waves also look as if there is a harmonic oscillator at every point in space, by the same logic of mode expansion. The descriptions are formally equivalent. This led people to believe that there is the luminiferous aether, because, how else could empty space carry the wave? But this turned out to be not true, there is no aether ...
Why do we need fermionic harmonic oscillators? And how is their ...
2017年11月18日 · A harmonic oscillator, whether it's bosonic or fermionic, is a single-particle state that can be occupied by noninteracting particles. A fermionic state can be occupied by one particle at most, while a bosonic state can be occupied by an unlimited number of particles.
Quantum Harmonic Oscillator propagator in Sakurai
2018年9月23日 · Harmonic Oscillator: extract the ground state wave function from the propagator. 1. Question on the State ...
harmonic oscillator - Definition of the $Q$ factor? - Physics Stack ...
$\begingroup$ By the way, I'm glad you asked this because it caused me to learn something very important: the resonance frequency of a damped harmonic oscillator is the frequency at which power flows from the driving force into the system but never the other way around. Take a look at the other question I cited at the bottom of my answer if you ...
Phase space density of $N$ harmonic oscillators
The result for the single oscillator follows from the usual method of counting states in phase space: $$ \Gamma_1 = \int \frac{dxdp}{(2\pi\hbar)}\;, $$ where the sub-script $1$ on $\Gamma_1$ means I am considering just one oscillator (in one dimension).
Solving the harmonic oscillator by using Hamilton-Jacobi formalism
2017年5月10日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.