# 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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### Why we taking $a = A \sin \phi$ and $b = A \cos\phi$ in place of constants in the Linear Harmonic Oscillator eq.?

The General Physical Solution of motion of the linear harmonic oscillator, $d^2x/dt^2 + \omega^2 x(t)= 0$ is $$x = a \cos \omega t + b \sin \omega t$$ where $a, b$ are two arbitrary real constants. ...
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### Can we think of spontaneous emission of a photon from an excited atom as a driven harmonic oscillator problem?

This is a kind of strange question, but I'm wondering, in the context of a fully quantum field theoretic treatment of spontaneous emission, if there is any model or way of calculating the process that ...
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### Compound pendulum - understanding torque of elastic force [closed]

Suppose I have the following system: The red "line" is a bar with $m=2kg$, $l=2m$, the two springs both have $k=6.1 \frac{N}{m}$. Now, if we displace the bar by $x$, we have the ...
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### Why is the commutator of ladder operators non-zero?

Griffiths states that the "ladder" of stationary states for a harmonic oscillator should be unique. That should mean that for one particular energy level, there exists only one energy state. ...
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### Why is the occupation of harmonic oscillator the Bose function?

Is there an intuitive reason why the occupation for the harmonic oscillator is the Bose distribution? I know that a QM-oscillator with commutation relations is a bosonic system but I have no intuition ...
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### Trouble determining initial phase in oscillations (two values for $\phi$)

I need to calculate the initial phase of a particle $m=4kg$ oscillating on the $x$ axis under the influence of $$F=\frac{- \pi x}{16}N,$$ if I know that when $t=2s$, the particle passes through the ...
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### Linear Harmonic motion (simple oscillator)

We know that for a simple harmonic linear oscillator, the displacement is given by $x(t)=A\sin(\omega t + \phi)$, where $\phi$ denotes the phase angle. Now as per my understanding this $\phi$ is only ...
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### Converting Displacement-Time to Distance-Graph for Simple Harmonic Motion

An object undergoes simple harmonic motion with the position/displacement function $$Position=\text{sin } t$$ The distance function is: \begin{equation} Distance = d(t)= \left\{ \begin{array}{lr} ...
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### Why does a larger radius of an oscillating sphere on a curved track result in a shorter period?

I understand the reason mathematically based on SHM of rolling spheres where T=2π√7(R-r)/5g But I don't know what is the theoretical explanation behind larger spheres being faster. I understand the ...
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### Is there a physical interpretation of the quadrature operators of the quantised EM field in a cavity?

I am considering a cavity setup using two mirrors perpendicular to the $z$-axis separated by a distance $L$, as seen here Assuming the electric field is polarised along the $x$-axis and uniform in ...
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### Evolution of Quantum Harmonic Oscillator into coherent state

Why does a quantum harmonic oscillator that is driven by an electromagnetic wave in cosine form with its frequency equal to the resonance frequency of the oscillator evolve from its groundstate into a ...
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### How can the quantisation of the energy of an oscillator be derived from the concept of entropy?

In quantum mechanics the energy of the harmonic oscillator is quantised, which means it can only take on discrete energy levels. In an equation: $$E_n = nhf$$ Planck did a lot of research on entropy. ...
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### Energy of polyatomic molecular vibrations

I understand that the energies of a simple diatomic molecular vibration are equal to $E_n=(n+\frac12)\hbar\omega$, and I also know the accompanying eigenfunctions for these energies. I have also heard ...
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### Energy of molecular vibrations

I have just read that the energy of a molecular vibration with frequency $\omega$ has eigenvalues of $(n+\frac12)\hbar\omega$, where $n$ is the quantum number. However, this equation really surprises ...
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### Near Resonant Behaviour

I'm reading Landau's Mechanics and on Chapter 5 on small oscillations he says in a footnote 'The "constant" term in the phase of the oscillation also varies". I am a bit confused as to ...
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