# 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 $(V_0/ω)^2 + X_0^2 = A^2$ in SHM? $V_0$ is initial velocity and $A$ is amplitude [closed]

In the SHM chapter of the HCV book, after deriving the expression $$V = \omega \sqrt{\left(\frac{V_0}{\omega}\right)^2 + X_0^2 - X^2},$$ the author simplifies it by substituting [\left(\frac{V_0}{\...
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### Reduced mass in a Harmonic Oscillator [closed]

I recently came across the harmonic oscillator and the concept of reduced mass, i.e $$\mu = \frac{m_1m_2}{m_1 + m_2}$$ To begin, I understand the derivation from the point of view of sitting on one ...
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### Fock Darwin wavefunction

The ground state of a 2D harmonic oscillator in magnetic field is a Gaussian wavepackets, and the spectrum of the Hamiltonian is solved by the Fock-Darwin states. Are there textbooks (I want textbooks,...
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### Tenth (even) harmonic of a open-closed tube

Can I say that a frequency (let's say f1) is the "tenth harmonic" of an open-closed tube? I would say it does not because closed tubes only have odd harmonics, is that correct??I want to ...
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### How to solve the 3 dimensional isotropic quantum harmonic oscillator with a non-zero natural length?

We are familiar with the Hamiltonian of a 3D isotropic harmonic oscillator $$H=\frac{1}{2m}\hat{p}^2+\frac{1}{2}m\omega^2r^2$$ where we assume the equilibrium point of this harmonic oscillator is at ...
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### Question regarding the half Harmonic Oscillator

In the normal Quantum Harmonic Oscillator (QHO), we normally use the operator method (because it's to elegant), but I recently discovered the problem in Griffiths (prob 2.42) where they ask the same ...
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### Velocity Formula in SHM

In Simple Harmonic Motion in one dimension, if we assume $$\text{Displacement}=x=A \text{sin} (\omega t+\phi)\implies \text{velocity}=v=A \omega \text{cos} (\omega t+\phi)$$ From here by substitution ...
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### How can you have position basis and energy basis? [duplicate]

In Quantum Mechanics, my understanding is that we have a Hilbert space. If we to model a particle in space we consider the space defined by the basis $$|x\rangle$$ for each $x \in \mathbb{R}$ We then ...
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### Interpretation of perpendendicularity of paths

Two particles are oscillating along two close parallel straight lines side by side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when their ...
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