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 Does Frequency Change With Damping (Underdamped Harmonic Oscillators) [closed]
I'm studying harmonic oscillators and I'm trying to model a system where both the frequency and amplitude decay over time. This is throwing me off because frequency decay is much less intuitive than ...
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How can I interpret the normal modes of this mechanical system?
How can I interpret the normal modes of this mechanical system?
The equations of motion for the system are as follows:
$$\left[\begin{array}{ccc}
m_{1}\\
& m_{2}\\
& & 0
\end{array}\...
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The period of simple harmonic motion [closed]
Am i understanding this correctly?
The harmonic oscillation of an object can be seen as the movement in the y direction along a circular path. So the time for one revolution around the circle will be ...
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What happens to the amplitude when a spring is compressed?
Say there's a spring lying on a horizontal table, with one end attached to a wall (say the left end) and it is in it's natural length. Now I compress the spring from the right end, and leave it. So ...
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Why Is There No Oscillator Representation for Operators in Planar ${\cal N}=4$ SYM Theory?
I'm studying the planar ${\cal N}=4$ Super Yang-Mills (SYM) theory and I'm curious about the representations of its operators, specifically the Hamiltonian and the dilatation operator. In many quantum ...
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Action-angle variables for three-dimensional harmonic oscillator using cylindrical coordinates
I am solving problem 19 of ch 10 of Goldstein mechanics. The problem is:
A three-dimensional harmonic oscillator has the force constant k1 in the x- and y- directions and k3 in the z-direction. Using ...
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When is minimum potential energy in simple harmonic motion not zero?
We know that in simple harmonic motion, potential energy is minimum at the mean position and it is zero since displacement is zero. So what are some cases in which minimum potential energy is not zero?...
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Article on 1D deformed quantum harmonic oscillator
Few years ago I was reading an article which I'm trying to find for quite some time but with no success so far. It was a paper about deformation of 1D quantum harmonic oscillator with continuous ...
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How is the quantum harmonic oscillator related to Fock states?
The question is basically in the title.
From what I understand, in the Fock state there is a certain number of particles in each energy level. The creation/annihilation operators create or destroy a ...
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If friction is not proportional to velocity, why do we model it as such when considering damped oscillations? [duplicate]
Early in our study of mechanics, we learn that friction is usually proportional only to normal force, without dependence on velocity. However, during our studies of damped oscillations, we often model ...
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Why am I getting this derivation of time period of pendulum in an accelerated frame wrong? [closed]
We are working in the frame of the cart and we are trying to obtain the $\tau=k\theta$ form.
So, let's write the $\tau=I_{axis}\alpha$ first for a small deviation $\theta$ from the vartical.
(The ...
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Potentials increasing faster than harmonic oscillator
I'm reading a book which says: (HO stands for harmonic oscillator):
The spectrum of the HO has equidistant energy eigenvalues. A potential that increases quicker than the HO has states which become ...
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Spherical quantum oscillator: Is energy smaller than the potential?
A particle with mass $m$ is inside the spherical quantum well $V(r)$:
\begin{equation}
V(r)=
\begin{cases}
-V_0, & \text{if}\ r<a \\
0, & \text{otherwise}
\end{cases} \...
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Understanding the dynamics of a perturbed quantum harmonic oscillator system
I'm trying to understand how quantum systems behave when they are perturbed, and I'm using the quantum harmonic oscillator as a model.
I start by implementing a symmetric gaussian shaped bump in the ...
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Investigation Results of Damping of A Spring Showing Changing Phase Angle? Why?
In an experiment I've recorded the displacement of the spring over time, investigating underdamped simple harmonic motion.
Using pre-existing formulae the data should conform to a curve of the form
$$...
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Infrared regularizing the harmonic oscillator path integral
This is from Laine and Vuorinen’s Basics of Thermal Field Theory. I do not understand why the fact that the integral over $x(\tau)$ implies the following regularization scheme. That is, I don’t ...
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Oscillating body and Doppler effect
Say we have a body attached to a spring, oscillating with some frequency $\nu$. This is one of the simplest problems studied in elementary Physics, and yet I've noticed we always study it positioning ...
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Regarding to the asymptotic solution of quantum harmonic oscillator
In quantum mechanics, the radial equation of the SHO takes the form
\begin{align}
\frac{d^2 u}{dx^2}+\left(\epsilon-x^2-\frac{l(l+1)}{x^2}\right)u=0,
\end{align}
where $x=\sqrt{\frac{m\omega}{\hbar}}r$...
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Two Simple Harmonic Motion (S.H.M.) in Perpendicular Direction
Suppose a particle is moving under the superposition of two S.H.M in the perpendicular direction... The general equation for the trajectory for the resultant motion arising due to the two component S....
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Can a harmonic oscillator never be Raman active?
Assuming we have some harmonic oscillator
\begin{equation}
H = \omega_0 (a^\dagger a + \frac{1}{2}) = \frac{p^2}{2m} + k x^2
\end{equation}
for which the excitations have even wavefunctions $\Psi_n(x)=...
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Closed expression for expected values of $\hat{p}\,\,^{2j}$ for the vacuum state
I am wondering if there is a closed expression for the expected value $\left<0\lvert \hat{p}\,\,^{2j}\lvert 0\right>$ with $j\in\mathbb{N}$, where $\left|0\right>$ is the vacuum state of the ...
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Quantum harmonic oscillator meaning
Imagine we want to solve the equations
$$
i \hbar \frac{\partial}{\partial t} \left| \Psi \right> = \hat{H}\left| \Psi \right>
$$
where $$\hat{H} = -\frac{\hbar^2}{2m} \frac{\partial^2}{\partial ...
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How can maximum kinetic energy not equal to total energy in SHM$?$ [closed]
A linear harmonic oscillator of force constant $2×10^6$$ \,\text{N}\,\text{m}^{-1}$ and amplitude $0.01 \,\text{m}$ has a total mechanical energy of $160 \,\text{J}$. Find ratio of maximum potential ...
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Generalizing Wave Equation to two strings connected at a point
Hi physics noob here with a question about strings.
I saw that you can derive the wave equation assuming an increasing density of masses and increasing spring constants in a 1-dimensional system of ...
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Quantum Harmonic Oscillator With a Linear "Perturbation"
It is well known that the energy solutions for the unidimensional quantum harmonic oscillator $V(x) = \frac{1}{2}m\omega^2x^2$ are $E_n = (n + \frac{1}{2})\hbar\omega, n \in \mathbb{N}$. In particular,...
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What are the different types of resonances in forced oscillation systems?
I'm currently studying resonances in systems subjected to forced oscillations and have come across various terms and cases that I'd like to understand more clearly. Specifically, I am analyzing a ...
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Physical meaning of Zero-Point Energy
I know that a quantum system can never have 0 energy due the Uncertainty Principle, and its lowest energy is called the Zero point Energy. However, Energy is a relative quantity (atleast in classical ...
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Derivation of Differential Equation of a Simple Pendulum [closed]
This pretty much a simple question and i seem to be making a dumb error here, but nonetheless I can't get the correct answer for the general equation of a pendulum which is :$$\ddot\theta=-\frac{g}{L}...
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Question regarding the half Harmonic Oscillator
In the normal Quantum Harmonic Oscillator (QHO), we normally use the operator method (because it's to elegant), but I recently discovered the problem in Griffiths (prob 2.42) where they ask the same ...
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Velocity Formula in SHM
In Simple Harmonic Motion in one dimension, if we assume
$$\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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