# 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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### Hamiltonian of quantum harmonic oscillator with $\psi(x)=\delta(x)$: comparison to classical mechanics

I was just reading the question Why can't $\psi(x)=\delta(x)$ in the case of a harmonic oscillator? The accepted answer says that $\psi(x)=\delta(x)$ is a mathematically valid state, though it's not ...
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### Are Thermal states Harmonic oscillators?

Excuse me if I use somewhat wrong terminology. But I've always been confused about this. So firstly when we talk about a 2-state system, like a qubit, it has dimension d=2, no? But what if we ...
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### Error propagation with a pendulum

The following is a 2018 F=ma exam question. I know that this isn't a homework site, but I think that my question is conceptually relevant. Here's the problem: A group of students wish to measure ...
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### Is the given system going to perform a simple harmonic motion? [closed]

The system shown in the picture consists of a spring of constant $k$, a pulley (disk) of mass $M$ and radius $R$ and a block of mass $m$ is let free from rest. There is no slipping between the rope ...
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### Simple harmonic question [closed]

consider a spring with a block of mass $m$ and spring constant $k$ that is inside a lift. the cable breaks and the lift falls freely. Show that the block now executes a simple harmonic motion of ...
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### If oscillatory motion is not simple (or chaotic), is it then by definition complex?

I'm trying to logically deduce or show that a specific type of motion is complex. It is two-dimensional oscillatory motion that can be expressed by coupled second order non-linear differential ...
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### Scalar product of squeezed coherent states

Consider two states of the type $|\alpha,\xi \rangle = \hat{D}(\alpha) \hat{S}(\xi) |0\rangle$, where $D$ and $S$ are the displacement and squeeze operators, respectively, and $|0\rangle$ is a 1D ...
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### Calculate weight of a barbell via measurement of period of oscillations

I have seen some videos on YouTube about some people that use "fake weights" in the gym, declaring to be able to lift much more weight than what is actually on the barbell. However, I think it should ...
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### Damped harmonic oscillator with different initial amplitudes

If a string under tension is plucked, and that string goes into underdamped harmonic oscillations, the graph of the exponential decay of the amplitude looks something like this: If I were to pluck ...
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### Relation between destruction/creation operators of harmonic oscillator in QM and Second Quantization

It is well known that in elementary QM the so-called destruction/creation operators $$a_i = \frac{Q_j + i P_j }{\sqrt{2}}, \quad a_i^* = \frac{Q_j - i P_j }{\sqrt{2}},$$ are introduced when ...
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### Why is this he correct? [closed]

Here is the question: "A spring stretches 0.4m when a 2kg mass is hung from it. The spring is stretched an additional 0.2m from its equilibrium point and is released. Determine: The Max ...
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### The simple harmonic oscillator model relating particles and fields in QFT

In all of the introductory Quantum Field Theory texts I gave read so far, (such as Zee, Srednicki, Luke), there is an introduction to the concept of fields as operators, following the simple harmonic ...
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### Harmonic oscillators in fluids and driven oscllations

If given a normal spring/mass system and letting the mass oscillate in a fluid say water, would it be possible for the motion of the fluid, if the fluid is moving to create a driven oscillation and ...
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### Equation of coupled springs : where does this potential come from?

In this document, we try to derive the equation of two coupled springs as in this picture. At the bottom of the page 2, they say : it would be more efficient to introduce the potential energy ...
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### When to use sine or cosine when computing simple harmonic motion

For simple harmonic motion (SHM), I am aware you can start of using either sine or cosine, but I am a bit confused as to when you would start off with sine rather than cosine. I know that a sine graph ...
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### What would be the minimum velocity of a particle performing S.H.M.?

We were asked a simple question on a test: What is the maximum and minimum velocity of a particle performing an SHM? Note here that we're talking about a generic standard SHM here. If the maximum ...
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### Energy of harmonic oscillators

I've calculated the energy of a classical harmonic oscillator (HO) as: \begin{align*} \overline E = \overline{E_K} + \overline{E_P} = \frac{\overline{p^2}}{2m} + \frac{k\overline{x^2}}{2} = \frac{...
The hamiltonian of the anisotropic HO e.g. in 2d is typically written as $$H=\frac{1}{2m}\left(p_x^2+p_y^2\right)+\frac{1}{2}m(\omega_x^2 x^2+\omega_y^2y^2)$$ What I wonder is why there is no ...