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.

329 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
7
votes
0answers
393 views

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 ...
7
votes
0answers
205 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-...
6
votes
0answers
87 views

Using perturbation theory or small oscillation approximation in Harmonic oscillator

Let us assume, we are given the following potential, $$V(x)=\frac{1}{2}ax^2-2x+\epsilon x^3$$ We need to find the energy levels of a particle bound in this potential Let us think of the ground level ...
5
votes
0answers
828 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 ...
5
votes
0answers
3k views

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 = \...
5
votes
1answer
1k 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 = \...
4
votes
0answers
86 views

Is there a spatial representation of the fermionic harmonic oscillator?

An answer to another question derives a Hamitonian of the fermionic harmonic oscillator in terms of a pair of position-like and momentum-like operators. These operators are, as expected, defined in ...
4
votes
0answers
79 views

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 ...
4
votes
0answers
197 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} = \...
4
votes
1answer
385 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}^...
4
votes
0answers
277 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 ...
4
votes
0answers
863 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-\...
3
votes
2answers
49 views

What are the maximum spring lengths of a double spring pendulum?

NOT a duplicate of Maximum length stretch of vertical spring with a mass?, I am asking about a system with two connected springs, as shown in this diagram For a single spring, you can simply equate ...
3
votes
0answers
47 views

Temporal stability of multimode coherent states

For the standard quantum harmonic oscillator, the coherent states $\{|\alpha\rangle, \alpha\in \mathbb{C}\}$ are temporally stable. That is, $$ e^{-iH t}|\alpha\rangle = |e^{-i t} \alpha\rangle, $$ ...
3
votes
1answer
70 views

Average energy of an SHM

Why do we usually calculate the average potential or kinetic energy of a simple harmonic motion with respect to time, why not with respect to position? Why even calculate average energy for an SHM? ...
3
votes
0answers
77 views

Harmonic oscillator in QFT

Given a single bosonic mode with frequency $\omega_0$, such that $\hat{H}=\hbar\omega_0(\frac{1}{2}+\hat{a}^{\dagger}\hat{a})$ how should one show the equivalence between the coherent state path ...
3
votes
0answers
65 views

Raising and Lowering Operators of a Hamiltonian

Lets say that I have a Hermitian Hamiltonian $H$ with a non-Hermitian raising operator operator $A$ which satisfies \begin{equation} [H,A] = \Omega A, \quad \Omega \in \ \mathbb{R}_{>0}. \end{...
3
votes
0answers
54 views

What do Grassmann-valued terms in operators really mean?

I've read (for example, ch. 5 of Piers Coleman's book on Many Body Physics), that a simple general formulation of a fermionic driven harmonic oscillator problem is: $$H = H_0 + V(t)$$ $$H_0 = E_0 c^\...
3
votes
0answers
40 views

Kinetic energy distribution by mass in mass-spring harmonic oscillator system

Basically I want to find a minimum working example of a non dissipative system that is able to concentrate kinetic energy on some subparts of the system. My first guess was to use the coupled ...
3
votes
0answers
91 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 ...
3
votes
0answers
232 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
votes
0answers
190 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\...
3
votes
0answers
235 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 ...
3
votes
0answers
333 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 ...
3
votes
0answers
779 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 $...
3
votes
0answers
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 ...
3
votes
1answer
225 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 ...
2
votes
2answers
61 views

Two masses connected by a spring

I have a question about a problem I saw on a website A mass is attached to one end of a spring, and the other end of the spring is attached to an immovable wall. The system oscillates with period T. ...
2
votes
1answer
68 views

Equivalent length of a simple pendulum

i was solving some question based on harmonic oscillations and a question popped up: If the angle between the the wires and the surface is 45 and the mass of the bob is $m$ calculate the time period ...
2
votes
0answers
20 views

How to perform the multi-scale analysis beyond harmonic oscillations?

I occasionally see this interesting method called multi-scale analysis. From what I understood, it is used to perturbatively solve a perturbed harmonic oscillator, meaning that the equation of motion ...
2
votes
0answers
39 views

Position/number uncertainty relation for the eigenstate of a Harmonic oscillator

Position and number operators for a Harmonic oscillator manifestly do not commute: $$ \hat{n}=a^\dagger a,\\ \hat{x}=\sqrt{\frac{\hbar}{2m\omega_0}}(a + a^\dagger),\\ [\hat{x},\hat{n}]= \sqrt{\frac{\...
2
votes
0answers
50 views

How do ladder operators in harmonic oscillator problem manage to accomplish this?

When we try to solve the harmonic oscillator problem by projecting the time independent equation onto position basis,we obtain solutions which do not vanish at infinity, then we ignore these solutions ...
2
votes
1answer
51 views

Optomechanical interaction

In cavity optomechanics, we see that if one of the mirrors is oscillatory and the other one is fixed,the photons are not able to shift the oscillating mirror continuously in one direction no matter ...
2
votes
0answers
32 views

Graphene in torsional penulum

I know damping occurs in a SHM torsional pendulum because the layers of the rope,string, etc. experience shearing forces between them. My first is question : 1. If something like a copper wire or rod ...
2
votes
0answers
136 views

Are electric and magnetic fields canonical conjugates?

When quantizing the electromagnetic fields in the context of quantum optics and quantum field theory, we often go for the vector potential $\mathbf{A}$ and its canonical momentum, which turns out to ...
2
votes
1answer
244 views

Using the uncertainty principle to estimate energies in ground states

Suppose for example we want to find the minimum energy of a particle undergoing simple harmonic motion. In classical mechanics, the energy is: $$E = \frac{p^2_x}{2m} + \frac{1}{2} m \omega_0^2x^2$$ ...
2
votes
0answers
121 views

Wick's rotation for the harmonic oscillator. Explicit computation

I'm stuck in this computation; it shouldn' be difficult but it's always better to check with a lot of details these things. Consider the propagator for the harmonic oscillator Ashok p.55 bottom of the ...
2
votes
0answers
55 views

Circuit quantization and energy dissipation

So when we do the procedure of circuit quantization we use the hamiltonian formalism which is only true when theres no dissipation. however we know real life circuits are dissipative , Im aware that ...
2
votes
0answers
81 views

Confusion on Quantum Harmonic Oscillator Eigenvalues

In standard PDE theory, one generates eigenvalues to Sturm-Liouville problems over a finite domain. So, for a wave equation, we have an infinite number of eigenvalues $\lambda_n$ for a Dirichlet ...
2
votes
2answers
305 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,...
2
votes
0answers
94 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: \...
2
votes
1answer
735 views

How the length, flexural rigidity and position of attached mass affects the period of oscillaion of cantilever?

Hey everyone, I'm a highschool student from New Zealand and can someone please explained to me with physics principles in words: Why increasing the length of cantilever increases the period of ...
2
votes
0answers
138 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 ...
2
votes
1answer
51 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 ...
2
votes
0answers
146 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}\...
2
votes
0answers
136 views

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. $...
2
votes
0answers
2k views

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 ...
2
votes
1answer
1k views

Why is the resonance frequency of an undamped oscillator equal to the undamped resonance?

I have read this post: 'How do you define the resonance frequency of a forced damped oscillator?' And I see that the resonant frequency occurs at the undamped oscillation frequency $\omega_0$ as ...
2
votes
0answers
2k views

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 ...
2
votes
0answers
505 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 ...

1
2 3 4 5
7