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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160 views

Experimental time-series for quantum particle-in-a-box or simple harmonic oscillator?

I would like to see experimental results for repeated measurement of a single-particle, quantum system that is approximately either particle-in-a-box or simple harmonic oscillator. If particle-in-a-...
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Kraus operators for two interacting harmonic oscillators: Problem with the calculation (Ex. 8.21 of Nielsen-Chuang)

I'm working with Exercise 8.21 of the Nielsen-Chuang book on quantum information. It illustrates the amplitude-damping quantum channel by the interaction between two harmonic oscillators (the first ...
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1answer
380 views

Energy Conservation of waves at a boundary

Consider a wave traveling on a string with velocity $\upsilon$ and mass density $\rho$ having unit length so that the mass of the string is $\rho$. Considering the string to be a simple harmonic ...
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635 views

Cubic perturbation to coupled quantum harmonic oscillators

I recently came across this two-dimensional problem of a particle in a potential of the form $$V = \displaystyle{\frac{1}{2}m \omega^2} \big(y^2 + x^2y \big) - \alpha y,$$ where $x$ and $y$ are known ...
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Energy Levels of 3D Isotropic Harmonic Oscillator (Nuclear Shell Model)

One simple way of detailing the very basic structure of the nuclear shell model involves placing the nucleons in a 3D isotropic oscillator. It's easy to show that the energy eigenvalues are $E = \...
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Modelling a pendulum with physical restrictions on it's range of motion

I'm currently working on a project based on suspension bridges and their oscillations. I've got an equation of motion for the movement of a pendulum as shown in the first image, I then wanted to be ...
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180 views

QFT-Style Lagrangian for a system of two symmetrized bosons

I'm wondering if anybody may have suggestions regarding the following problem. The Hamilton operator of the quantum harmonic oscillator (QHO) can be written as follows: $$ \hat{\mathcal{H}}_{QHO} = \...
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253 views

Damped quantum harmonic oscillator - evolution of coherent state

I am trying to solve the following Master equation (also similar to damped quantum harmonic oscillator): $$\frac{d\hat{\rho}}{dt} = \frac{\Gamma}{2}\left(2\hat{a}\hat{\rho}\hat{a}^{\dagger} - \hat{a}^...
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257 views

Equivalency of $Q$ Factor Definitions

The Q factor is defined (seemingly) as $$Q=2\pi\frac{\mathrm{energy \, \, stored}}{\mathrm{energy \, \,dissipated \, \, per \, \, cycle}}$$ however on Wikipedia is says that the Q factor can be ...
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251 views

The Hamiltonian for clocks?

I am rather a theoretician and looking for a formalism to represent biological clocks by Hermitian operators. The simplest thought model I am looking for is a formal representation of a clock (for ...
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768 views

Relativistic genarization of Quantum Harmonic Oscillator

I am trying to find out relativistic description of a quantum harmonic oscillator. For a classical relativistic oscillator mass is a function of co-ordinates(http://arxiv.org/abs/1209.2876). $$m(x)=m-\...
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1answer
965 views

Zero-point energy amplitude calculation

On this page https://www.miniphysics.com/simple-harmonic-oscillator.html It is stated that for a linear restoring force of $F = -k \Delta x$, the total energy is $ E = K + U $ or rather $ \\ E = \...
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66 views

Harmonic Oscillator and Shifts in Derivative Operators

What symmetries/symmetry breaking arises from shifts in the derivative operators? To explain what I mean let's study an example. The classical one particle one dimensional harmonic oscillator has the ...
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143 views

Path integral measure for propagator of harmonic oscillator

I've been looking at the path integral + saddle point method derivation of the propagator of the harmonic oscillator recently, and I came to conclusion that the measure bit of the path integral ...
3
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1answer
196 views

Does the brightness of day follow simple harmonic 'motion'?

Is it really true that the brightness during the day on earth follows simple harmonic motion? My teacher mentioned this as an example but it doesn't feel obvious to me by any stretch of the ...
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1answer
926 views

Damping coefficient and damping ratio

I am not sure if I understand the term damping coefficient correctly (I am a high-school student). Here's the link for the info that I learned: http://hyperphysics.phy-astr.gsu.edu/hbase/oscda.html ...
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180 views

Creating an arbitrary state of the quantum simple harmonic oscillator

Suppose $\mathcal{B}=\{|0\rangle, |1\rangle, |2\rangle, ... \}$ is the energy eigen-basis of a quantum simple harmonic oscillator. I want to create the state \begin{equation} |\Psi\rangle = c_{0}|0\...
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205 views

Driven-damped oscillator: deduce the phase and/or resonant freq from amplitudes at varying freqs

Suppose that we have a fairly standard driven-damped harmonic oscillator (i.e. linear spring restoring force, linear damping force, sinusoidal driving force, etc). The catch is: we don't know the ...
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305 views

Measure energy state of quantum harmonic oscillator

When discussing the quantum mechanical harmonic oscillator we are talking about energy eigenstates. How would one actually measure in which state an harmonic oscillator is in? Could you weigh it and ...
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759 views

Amplitude of a Forced Harmonic Oscillator

For an assignment in one of my maths units at uni, I've been asked to derive and solve the differential equation of motion for a forced harmonic oscillator, with the forcing function having the form $...
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2k views

Damping and stiffness constants of water

I'm working on a simulation of water drops falling into a pool. I'm specifically interested in the waves generated by the impact of the drops. In order to calculate the vertical motion of the waves, I ...
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39 views

What is the force that makes the wave return to its equilibrium point?

The thing is, the force in simple harmonic motion is clear to me. it is the opposite direction of the movement of the object. F=-kx I assume that the force that makes the wave going down is gravity....
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1answer
100 views

Simple Pendulum in Cartesian Coordinates

Riffing on the question in Simple Pendulum Why Generalized Coordinate Always Angle? , I'm trying to write down Newton's law for a simple pendulum in Cartesian coordinates. (I'm doing this as an ...
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49 views

If there are eigenstates of $L_z$ in a degenerate subspace, are there also eigenstates of $L^2$?

The question arises from an exercise but tackles deeper understanding of angular momentum operators. Suppose we have a 2D harmonic oscillator and an infinite square well in the third dimension: \...
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90 views

Pulse excitation of damped harmonic oscillator: delayed maximal response

When a damped harmonic oscillator (HO) is excited by a pulse (Gaussian*sinusoid), the maximum of the oscillating response is delayed. This make sense because the impulse response $h(t)$ of the HO is ...
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1answer
46 views

Particle ensemble performing shm, calculate amplitude pdf

Consider the shm for a single particle. Then the particle's position is given by (assume zero initial phase): $$x = a \times \sin(\omega t)$$ The infinitesimal probability of finding a particle ...
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104 views

Ordering of energy levels of bound states of central potential

I have been attempting to solve the following central potential using schrodinger equation.$$V(r)=a_{1}r^{2}+\frac{a_{2}}{r^{2}}+a_{3}$$ The radial equation becomes, $$\Bigg[\frac{-\hbar^{2}}{2m}\...
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Prove that the position-space representation of a single particle wave function is given by $e^{i \textbf{p}\cdot\textbf{x}}$

I'm trying to prove that the position-space representation of a single particle wave function of the state $|\textbf{p}⟩$ in Quantum Field theory is given by $e^{i \textbf{p}\cdot\textbf{x}}$ i.e. $...
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Degenerate perturbation theory of a two-dimensional harmonic oscillator

In short: how should one develop perturbation theory, when all the values $\langle a | \delta H | b \rangle$ vanish in some manifold of degenerate states $a$, $b$? A more concrete and longer ...
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Correlation function for the ground state of simple harmonic oscillator

I calculated correlation function $C(t)=\langle x(t)x(0)\rangle$ for ground state of Simple Harmonic Oscillator (SHO) in two different methods. But the results do not match. First Attempt: From ...
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406 views

Why is the quantum harmonic oscillator model used when an electromagnetic field is quantised?

I'm reading textbooks for quantum optics, and then see that every textbook introduces the quantisation of light, for which each book employs the quantum harmonic oscillator model. Why is this ...
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223 views

Finding the state and wave-function for two identical spin-1 bosons trapped in one-dimensional harmonic oscillator

My question concerns the validity of my approach to a problem and wether the answer is correct. I am tasked with writing the state vector(s) and wave-function(s) for when two identical spin-1 bosons ...
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394 views

Dipole of a Particle in Quantum Harmonic Potential Subject to Electric field

Consider a quantum particle in harmonic potential subject to electric field in the positive $x$ direction. The Hamiltonian of this system has the form $$\hat{H}=\frac{1}{2}m\omega^{2}\hat{x}^{2}-qE\...
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Supersymmetric Bogoliubov transformation

Given the simplest system containing one bosonic and one fermionic degree of freedom with the Hilbert space spanned by \begin{align} |n,m\rangle\quad\text{with}\quad n\in\mathbb{N}\quad\text{and}\quad ...
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283 views

Are there exact expressions for the Floquet states of a periodically-forced, undamped harmonic oscillator?

For this question I was looking for the Floquet states of a quantum harmonic oscillator driven by a non-resonant harmonic force, and I had a rather harder time finding it than the simplicity of the ...
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1answer
1k views

Motion of Thompson's jumping ring

Thompson's jumping ring experiment is set up as follows: There is a force acting on the ring $F(x)$ where $x$ is the vertical displacement. The force is due to the $90^\circ$ out of phase flux ...
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1answer
227 views

Response functions for the quantum harmonic oscillator

I'm going through problems in Quantum Field Theory for the Gifted Amateur, and have been trying to understand a problem on the forced quantum oscillator [$L = \frac{1}{2}\dot{x}(t)^2-\frac{1}{2}m\...
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195 views

What are you studying when you study a Harmonic Oscillator in QM?

This probably is a naive question - so please forgive a self-studier. In the text I am studying, one builds a HO by placing a particle in a potential that increases quadratically from the origin. The ...
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498 views

Degeneracy, spherical harmonics

In a 3D oscillator, the energy levels are known to be $(n_x + n_y + n_z + \frac{3}{2})\hbar \omega = (n + \frac{3}{2})\hbar \omega$. Say for $n = 1$, any of the $n$'s can be $1$ and the rest are $0$. ...
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226 views

Mean energy harmonic oscillator

I know that for a particle under the potential $$V(x,y,z)=\frac{k}{2}(x^2+y^2+z^2)$$ the equipartition theorem says that it contributes to the mean energy to $\frac{3k_BT}{2} $ (one half for each ...
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Is there an equation that tells you more about the amplitude of an object which is in resonance?

I'm a high school senior and I have to write a paper about resonance and differential equations. I've been searching the Internet for a long time, but I haven't found an equation that is properly ...
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1answer
205 views

Simulation of oscillator with frequency dependent damping

What would be the equation for the frequency dependent damping of harmonic oscillator? Is there something like: $$ \ddot{x}+2\delta\dot{x}+\omega_0^2x = \frac{F}{m}f(t) $$ with frequency dependent ...
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2answers
29 views

The effect of tension force on a pendulum swinging in simple harmonic motion

In physics class, I learned that the reason a pendulum moves about the equilibrium position is due to the force acting towards the center, which is the resultant force of tension and weight. However,...
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44 views

3D harmonic oscillator magic numbers

I know that, $$V(r) = (1/2) m \omega^2 r^2 ,$$ $$\omega \approx 40(Z+N)^{-1/3}\ \rm{MeV} $$ and $$E = (n+3/2) \hbar \omega.$$ How do you find the magic numbers of protons and neutrons which ...
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Why does light come as quanta of the harmonic oscillator?

I've recently been learning the basics of Quantum optics and it seems to be a fundamental concept that light is best described in the framework of the Quantum Harmonic Oscillator. This lead to a ...
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1answer
29 views

Proving that motion of an $n$ dimensional oscillator can be written as a linear combination of “sine waves”

Here is a related question which might provide some context: LINK. Let's consider an oscillator with equation of motion in $n$ dimensions: $$ \frac{d^2}{dt^2} \vec{x} = K \vec{x}. $$ Given that $\...
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2answers
142 views

Difference between Oscillatory motion and vibratory motion

What is the difference between oscillatory motion and vibratory motion. I have read in my book that "If the amplitude of oscillatory motion is extremely small,the motion is called vibratory motion". ...
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27 views

Spring oscillation model

When a spring - in real world - is extended $Xo$ from its natural position, it oscillates and eventually decreasing it's amplitude with time, comes to a stop. Is this a damped system or no? If yes how ...
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1answer
36 views

Trouble following a chapter on harmonic oscillators (classical mechanics 5th edition)

I'm following Classical Mechanics, 5th Edition by Tom W.B. Kibble and Frank H. Berkshire. I'm following it since I'm interested in studying physics (although, am doing it at home myself). I've worked ...
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2answers
56 views

Why does angular frequency of a particle in SHM does not change when it's velocity is changed

$V = A \omega \sin(\omega t + \theta)$ gives velocity of a particle in SHM at time $t$. But, why does the value of $\omega$ doesn't change when $V$ is changed?