# 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 to as toy problems that describe many physical systems.

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### Experimental time-series for quantum particle-in-a-box or simple harmonic oscillator?

I would like to see experimental results for repeated measurement of a single-particle, quantum system that is approximately either particle-in-a-box or simple harmonic oscillator. If particle-in-a-...
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### Kraus operators for two interacting harmonic oscillators: Problem with the calculation (Ex. 8.21 of Nielsen-Chuang)

I'm working with Exercise 8.21 of the Nielsen-Chuang book on quantum information. It illustrates the amplitude-damping quantum channel by the interaction between two harmonic oscillators (the first ...
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### Energy Conservation of waves at a boundary

Consider a wave traveling on a string with velocity $\upsilon$ and mass density $\rho$ having unit length so that the mass of the string is $\rho$. Considering the string to be a simple harmonic ...
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### Cubic perturbation to coupled quantum harmonic oscillators

I recently came across this two-dimensional problem of a particle in a potential of the form $$V = \displaystyle{\frac{1}{2}m \omega^2} \big(y^2 + x^2y \big) - \alpha y,$$ where $x$ and $y$ are known ...
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### Degenerate perturbation theory of a two-dimensional harmonic oscillator

In short: how should one develop perturbation theory, when all the values $\langle a | \delta H | b \rangle$ vanish in some manifold of degenerate states $a$, $b$? A more concrete and longer ...
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### Correlation function for the ground state of simple harmonic oscillator

I calculated correlation function $C(t)=\langle x(t)x(0)\rangle$ for ground state of Simple Harmonic Oscillator (SHO) in two different methods. But the results do not match. First Attempt: From ...
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### Why is the quantum harmonic oscillator model used when an electromagnetic field is quantised?

I'm reading textbooks for quantum optics, and then see that every textbook introduces the quantisation of light, for which each book employs the quantum harmonic oscillator model. Why is this ...
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### Finding the state and wave-function for two identical spin-1 bosons trapped in one-dimensional harmonic oscillator

My question concerns the validity of my approach to a problem and wether the answer is correct. I am tasked with writing the state vector(s) and wave-function(s) for when two identical spin-1 bosons ...
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