# 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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### How is harmonic motion (specific and not a special case) different from periodic motion? [duplicate]

I have seen written in many books that a motion that repeats itself after a specific time period follows periodic or harmonic motion. However I know for a fact that damped harmonic motion cannot ...
2answers
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### Problem with spring oscillator measurement - inconsistent frequency

I measured the periodic movement of a spring with a mass and plotted it Looking at the first graph, I assumed the frequency is somewhere between 2-2.5 Hz. The mass hanged on spring was 100 g. Using ...
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### How to properly find the spectrum of the Quantum Harmonic Oscillator? [duplicate]

We want to find the spectrum of the Harmonic Oscillator Hamiltonian: $$H=\frac{\hat{p}^2}{2m}+\frac{1}{2}m\omega ^2 \hat{x}^2$$ From what I have seen in many books the procedure is as follows: We can ...
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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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### Is there any phase delay between displacement and driving force in undamped driven oscillation when the driving frequency is below resonant frequency?

I know that there is phase delay in damped driven oscillation but I want to know is there any phase delay in undamped driven oscillation when we apply sinusoidal driving force. When driving force is ...
1answer
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### Restoring force of electron-nucleus spring model (Lorentz oscillator model)

The restoring force should fulfill at least two criterion Experience repulsive force when it is compressed and attractive force when it is extended The restoring force always increases with distance ...
2answers
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### Is there any effect that draws the oscillation frequencies of two particles together?

I'm looking for any sort of coupling that draws oscillation amplitudes together if one couples two (nearly) harmonic oscillators, basically the opposite of avoided crossing or level repulsion. Is ...
0answers
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### Pendulum Tuned Mass Damper - Mathematical Relationship between Mass and Damping Ratio

I am doing an experiment where I built a test tower with a pendulum to act as a tuned mass damper, similar to this picture below: I want my independent variable to be the mass of the pendulum (which ...
1answer
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### Why is a phase shift through a time delay not used for damping in vibration dampers?

Why do oscillation dampers use signal conversion through a sufficiently massive electrical circuit (with resistors, capacitors, diodes) to create antiphase, instead of simply shifting the signal in ...
0answers
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### Matter wave coherence length

Coherence length is defined as (see here) The propagation distance over which a coherent wave (e.g. an electromagnetic wave) maintains a specified degree of coherence. Other questions see here, and ...
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### How can you approximate number of bound states in a harmonic oscillator potential $V$ and also for a Dirac delta function using uncertainty principle?

How can you approximate the number of bound states in a harmonic oscillator potential $V$ and also for a Dirac delta function using the uncertainty principle?
1answer
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### What is my misunderstanding in Wick's theorem?

Trying to understand Wick's theorem, I took most of my knowledge from the corresponding Wikipedia article. The statement is that given the definition of normal ordering of operators $A,B,C,\ldots$ any ...
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### Confusion about modes and quantum field theory

I'm learning quantum field theory from P&S and Srednicki. I'm having a lot of difficulties understanding the concept of a momentum state. In particular, I'm confused about how to interpret the ...
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### Transformation between two different sets of molecular vibrational normal coordinate systems [migrated]

Lets assume we have $N$ Atoms and we treat them within the Born-Oppenheimer Approximation. We can calculate the adiabatic electronic groundstate potential. Lets assume we observe two local minima, ...
1answer
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### Why do you add independent solutions when finding a general equation for SHM?

In my physics class, we have an assignment based on simple harmonic motion with the differential equation: $$\frac{d^2x}{dt^2} + a\frac{dx}{dt} + a^2x = 0$$ Different parts of the question help us ...
1answer
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### Identical particles placed on the energy levels of a 1D harmonic oscillator

If the particles are 6 spinless bosons, would they tend to occupy the ground state together and make the lowest total energy of the system $E=6E_0=3 \hbar \omega$? And If the particles are 6 spin 1/2 ...
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### The infinite-fold degeneracy of an oscillator when becoming a free particle

Considering a one-dimensional case, and if it has the following relation: $$(1) : [H,a]= \pm \omega a$$ then there are evenly spaced spectrum lines. If we sink $\omega \rightarrow 0$ , or, ...
0answers
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### Can different quantum field oscillators have different frequencies $ω_k$? [closed]

Can different quantum field oscillators have different frequencies $ω_k$? If so, does it follow from that the energy gaps between two neighboring eigenvalues $ℏω_k$ could be different for different ...
1answer
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### Statistical weight for $N$ harmonic oscillators in microcanonical ensemble

I would like to compute the statistical weight for the microcanonical ensemble for $N$ harmonic oscillators. To do that i use the hamiltonian of the harmonic oszillator: H(q,p)=\sum\limits_{i=1}^N \...
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### Transmon: why do we need unharmonic hamiltonian to isolate energy levels? [duplicate]

With a quantum harmonic oscillator, we cannot isolate energy levels, e.g. to create a qubit. We need to embed anharmonicity, to get unevenly-spaced energy levels and so making them distinguishable. ...
1answer
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### Proof that body performs SHM

At core, SHM is the shadow of a particle revolving with omega on a circle of radius equal to amplitude. Now we say that body performs SHM either if the equation of its position makes a sinusoidal ...
0answers
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### Using operators to solve SHO with $x^2$ perturbation

I have simple harmonic oscillator potential:$V_0 =\frac{1}{2} m\omega^2x^2$. So the Hamiltonian is: $H_0=\frac{p^2}{2m}+\frac{1}{2} m\omega^2x^2$. We now add a perturbation which is \$V_1 =\frac{1}{2} \...