# 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 is the harmonic oscillator so important?

I've been wondering what makes the harmonic oscillator such an important model. What I came up with: It is a (relatively) simple system, making it a perfect example for physics students to learn ...
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### Are there pure sine waves in nature or are they a mathematical construct that helps us understand more complex phenomena?

I've studied a bit of frequency analysis with FFT and optimal phase binning and was taught that we can represent any composite waveform as the sum of its component frequencies. I understand the maths ...
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### Hilbert space of harmonic oscillator: Countable vs uncountable?

Hm, this just occurred to me while answering another question: If I write the Hamiltonian for a harmonic oscillator as $$H = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 x^2$$ then wouldn't one set of ...
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### Why does a simple pendulum or a spring-mass system show simple harmonic motion only for small amplitudes?

I've been taught that in a simple pendulum, for small $x$, $\sin x \approx x$. We then derive the formula for the time period of the pendulum. But I still don't understand the Physics behind it. Also, ...
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### Why doesn't my kitchen clock violate thermodynamics?

My kitchen clock has a pendulum, which is just for decoration and is not powering the clock. The pendulum's arm has a magnet that is repelled by a second magnet that is fixed to the clocks body. The ...
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### Intuition - why does the period not depend on the amplitude in a pendulum?

I'm looking for an intuition on the relationship between time period and amplitude (for a small pertubation) of pendulums. Why does the period not depend on the amplitude? I know the math of the ...
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### “QFT is simple harmonic motion taken to increasing levels of abstraction”

"QFT is simple harmonic motion taken to increasing levels of abstraction." This is my memory of a quote from Sidney Coleman, which is probably in many textbooks. What does it refer to, if he meant ...
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### Why Don't the Ladder Operators Commute?

I have two problems with ladder operators. The first is that I feel they should somehow result in measurable things. The asymmetry of applying the plus operator versus the minus operator is very ...
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### Simple Harmonic Motion - What are the units for $\omega_0$?

I'm trying to understand the units in: $$mx''+kx=0$$ And the general solution is $$x(t)=A \cos(\omega_0 t)+B \sin(\omega_0 t).$$ Let $\omega_0 =\sqrt{\frac{k}{m}}$ - the unit for the spring ...
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### Eigenstates of a shifted harmonic oscillator

Let's say I have a quantum harmonic oscillator $H = \omega a^\dagger a$, where $a^\dagger$ is the raising operator and $a$ is the lowering operator and $H |n\rangle = \omega n |n\rangle$. Now assume ...
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### Will a damped harmonic oscillator, with no initial amplitude, oscillate if there was background “noise”?

Suppose I have a damped harmonic oscillator which is at rest, sitting comfortably with no initial amplitude, obeying the equation $$\ddot{x} + \frac{1}{Q}\dot{x} + x = 0$$ where x is the vertical ...
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### What's a good reference for this classical picture Feynman's talking about?

I have a mathematics background but am trying to educate myself a little about physics. At the beginning of Feynman's QED book (not the popular one) is the following: Suppose all of the atoms in ...
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### Book recommendations for second quantization

I am trying to familiarize myself with the ideas of second quantization. However, the literature that I can find online seems only to outline the tools of this formalism of quantum mechanics. ...
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### Constant magnetic field applied to a quantum harmonic oscillator

I have a spinless particle of mass $m$ and charge $q$ which is an isotropic harmonic oscillator of frequency $\omega_0$, then I apply a constant magnetic field in the $z$ direction. We can show the ...
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### Correct way of solving the equation for simple harmonic motion

I am considering the equation for simple harmonic motion, which is $\ddot x +\omega ^2x=0$ To solve this, I have seen three approaches. This is confusing as I do not know which approach is physically ...
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### Limit as $x_1 \to x_0$ for the propagator of the harmonic oscillator

Consider a non-relativistic particle of mass $m$, moving along the $x$-axis in a potential $V(x) = m\omega^2x^2/2$. use path-integral methods to find the probability to find the particle between $x_1$ ...
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### Is the vacuum state a coherent state?

I'm asking because I got introduced to the state $|0\rangle$ as a fock-state. Nevertheless: $$\hat{a} |0\rangle = 0 |0 \rangle$$ It is an eigenstate of $\hat{a}$ with eigenvalue $0$, and it can be ...
### Why does the acceleration $g$ due to gravity not affect the period of a vertically mounted spring?
For a vertically mounted spring, I was looking at the formula $T= 2\pi \sqrt{m/k}$ for a period. Why doesn't the gravitational acceleration $g$ factor in?