Questions tagged [harmonic-oscillator]
The term "harmonic oscillator" is used to describe any system with a "linear" restoring force that tends to return the system to an equilibrium state. There is both a classical harmonic oscillator and a quantum harmonic oscillator. Both are used as toy problems that describe many physical systems.
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Is zero-point energy a mathematical artifact?
From Wikipedia, Pauli has said in his Nobel lecture that "It is clear that this zero-point energy has no physical reality". This feels natural - I've always been slightly puzzled by the ...
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Mass lifting off a harmonic oscillator
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 ...
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Harmonic oscillators and bead in a parabolic wire
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 ...
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What is the energy spectrum of two coupled quantum harmonic oscillators? [duplicate]
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{...
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Matrix method for solution of amplitudes in the beaded string problem
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 ...
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Can someone show that the thermodynamic limit $N\to\infty$ is a singular limit, and thus the limits are non-commuting?
Can someone work out the limits and show indeed that the limit is singular?
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Transforming wavefunction from energy basis to annihilation operator basis for quantum harmonic oscillator
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:
$$
|\alpha \...
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Boltzmann correction factor for free particles but not for harmonic oscillators?
A) Suppose the microcanonical statistical mechanics of $N$ one-dimensional identical free particles of mass $m=1/2$, in an interval of size $L$. We must integrate over $2N$-dimensional phase space in ...
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Creation of a Sinusoidal wave from a body undergoing SHM
Imagine a plane of paper in $xy$ plane and a pen kept at the origin undergoing SHM in the $y$-direction. Would it be possible to give the pen some horizontal acceleration for it to trace a sinusoidal ...
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The Klein-Gordon equation as a limit of continuous coupled harmonic oscillators?
I've seen espoused at the very least a metaphor between the discrete system of $n$ coupled harmonic oscillators
$$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}\...
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Expectation value of anticommutator $\{x(t),p(t)\}$ in harmonic oscillator
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 ...
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About the absorption coefficient
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 ...
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What is the difference between these two transformations concerning phonons?
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 ...
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What are realistic parameters values for a molecule in a viscous medium?
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, ...
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Regularization of determinants in QFT
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 ...
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