# 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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### 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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### 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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### Using perturbation theory or small oscillation approximation in Harmonic oscillator

Let us assume, we are given the following potential, $$V(x)=\frac{1}{2}ax^2-2x+\epsilon x^3$$ We need to find the energy levels of a particle bound in this potential Let us think of the ground level ...
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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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### Is there a spatial representation of the fermionic harmonic oscillator?

An answer to another question derives a Hamitonian of the fermionic harmonic oscillator in terms of a pair of position-like and momentum-like operators. These operators are, as expected, defined in ...
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### Modelling a pendulum with physical restrictions on it's range of motion

I'm currently working on a project based on suspension bridges and their oscillations. I've got an equation of motion for the movement of a pendulum as shown in the first image, I then wanted to be ...
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### The Hamiltonian for clocks?

I am rather a theoretician and looking for a formalism to represent biological clocks by Hermitian operators. The simplest thought model I am looking for is a formal representation of a clock (for ...
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### Kinetic energy distribution by mass in mass-spring harmonic oscillator system

Basically I want to find a minimum working example of a non dissipative system that is able to concentrate kinetic energy on some subparts of the system. My first guess was to use the coupled ...
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### Harmonic Oscillator and Shifts in Derivative Operators

What symmetries/symmetry breaking arises from shifts in the derivative operators? To explain what I mean let's study an example. The classical one particle one dimensional harmonic oscillator has the ...
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### Path integral measure for propagator of harmonic oscillator

I've been looking at the path integral + saddle point method derivation of the propagator of the harmonic oscillator recently, and I came to conclusion that the measure bit of the path integral ...
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### Creating an arbitrary state of the quantum simple harmonic oscillator

Suppose $\mathcal{B}=\{|0\rangle, |1\rangle, |2\rangle, ... \}$ is the energy eigen-basis of a quantum simple harmonic oscillator. I want to create the state |\Psi\rangle = c_{0}|0\...
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### Driven-damped oscillator: deduce the phase and/or resonant freq from amplitudes at varying freqs

Suppose that we have a fairly standard driven-damped harmonic oscillator (i.e. linear spring restoring force, linear damping force, sinusoidal driving force, etc). The catch is: we don't know the ...
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### Measure energy state of quantum harmonic oscillator

When discussing the quantum mechanical harmonic oscillator we are talking about energy eigenstates. How would one actually measure in which state an harmonic oscillator is in? Could you weigh it and ...
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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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### Why is the resonance frequency of an undamped oscillator equal to the undamped resonance?

I have read this post: 'How do you define the resonance frequency of a forced damped oscillator?' And I see that the resonant frequency occurs at the undamped oscillation frequency $\omega_0$ as ...
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 ...