Questions tagged [harmonic-oscillator]

Question 1

Consider this setup: A classic, harmonic oscillator made of a spring with spring constant $k$ and a mass $m_1$ that oscillates vertically. $m_1$ is formed like a horizontal plate, and on the plate ...

Question 2

I have a question about what in the abstract derivation we cannot assume for the system of a bead in a parabolic wire when we do not consider small displacements. (1) We want to consider a system in ...

Question 3

I am familiar with the single quantum harmonic oscillator: using either the algebraic ladder-operator method or by solving the Schrodinger equation, one obtains the well-known energy spectrum \begin{...

Question 4

The beaded string problem, in which we have a massless string fixed at both ends, has beads uniformly placed on it, all distance $a$ apart. The string is given transverse motion. Assuming small ...

Question 5

Can someone work out the limits and show indeed that the limit is singular?

Question 6

I want to write $|n\rangle$ in the basis of eigenstates of $\hat a$. Here $|n\rangle$ is the $n^{th}$ energy eigenstate of quantum harmonic oscillator. To do this, first of all we know: $$ |\alpha \...

Question 7

A) Suppose the microcanonical statistical mechanics of $N$ one-dimensional identical free particles of mass $m=1/2$, in an interval of size $L$. We must integrate over $2N$-dimensional phase space in ...

Question 8

Imagine a plane of paper in $xy$ plane and a pen kept at the origin undergoing SHM in the $y$-direction. Would it be possible to give the pen some horizontal acceleration for it to trace a sinusoidal ...

Question 9

I've seen espoused at the very least a metaphor between the discrete system of $n$ coupled harmonic oscillators $$L = \sum_i^n \frac{1}{2}m_i \dot{x}_i^2 - \frac{1}{2}k_i(x_{i+1}-x_i)^2 -\frac{1}{2}\...

Question 10

I am reading a book on Q.M (Konishi-Paffuti A new introduction to Quantum Mechanics) and at some point they want to calculate $\left\langle p(t)^2\right\rangle$ for the harmonic oscillator using the ...

Question 11

The absorption coefficient is calculated for a monochromatic field interacting with a stationary ensemble of two-level atoms by solving the steady-state density matrix and determining the field's ...

Question 12

Given a Hamiltonian of $N$ particles coupled as harmonic oscillators $$ H = \sum_{j = 1}^N \frac{p_j^2}{2 m} + \frac{1}{2} \sum_{j,k = 1}^N C_{j k} x_j x_k $$ where $C_{j k} = C_{k j}$, i.e. symmetric ...

Question 13

I have been scouring through the internet to find any source that explicitly states the constant parameters used for simulating a simple molecular system like the one I'm interested in currently, ...

Question 14

I have a question regarding regularization in quantum field theory. Hagen Kleinert talks about analytic regularization in his book "Path Integrals". In chapter 2.15 he calculates the ...

Question 15

Consider a system of three masses (all $m$) connected by four springs (all with spring constant $k$), and the ends are fixed to walls, like ...

Stack Exchange Network

Questions tagged [harmonic-oscillator]

Mass lifting off a harmonic oscillator

Harmonic oscillators and bead in a parabolic wire

What is the energy spectrum of two coupled quantum harmonic oscillators? [duplicate]

Matrix method for solution of amplitudes in the beaded string problem

Can someone show that the thermodynamic limit $N\to\infty$ is a singular limit, and thus the limits are non-commuting?

Transforming wavefunction from energy basis to annihilation operator basis for quantum harmonic oscillator

Boltzmann correction factor for free particles but not for harmonic oscillators?

Creation of a Sinusoidal wave from a body undergoing SHM

The Klein-Gordon equation as a limit of continuous coupled harmonic oscillators?

Expectation value of anticommutator $\{x(t),p(t)\}$ in harmonic oscillator

About the absorption coefficient

What is the difference between these two transformations concerning phonons?

What are realistic parameters values for a molecule in a viscous medium?

Regularization of determinants in QFT

Why is a symmetric matrix necessary when finding normal modes?

Hot Network Questions