The term "harmonic oscillator" is used to describe any system with a "linear" restoring force that tends to return the system to a 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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Vibration of pulley and string system

So here's the statement: A pulley of a mass $M$ is hanged using a spring (stiffness of the string being $k_1$), as shown in the image. What is the frequency of the pulley's oscillation? So that's ...
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Does spatial coupling prohibit resonances due to an external source field?

The harmonic oscillator coupled to a sinodial external source $$\tfrac{\partial^2 x(t)}{\partial t^2}+\omega_0^2 x(t)=F_0\sin(\omega_\text{ext}\ t),$$ has the solution $$x(t)=x(0)\cos(\omega_0 t)+C ...
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How can I derive the Hamiltonian of simple harmonic oscillator from this Lagrangian?

I'm working through Leonard Susskind's Theoretical Minimum: Classical Mechanics and I can't seem to understand how the Hamiltonian of a simple harmonic oscillator is derived from the following ...
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Questions related to resonance/standing-waves and sound

I understand resonance for a simple harmonic oscillator but not for more complex systems like standing waves. How can I be in resonance with the normal mode in an organ pipe? I understand that the ...
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Energy of damped harmonic oscillator begins to increase with very large Q in numerical integration

I have numerically integrated the (reduced) homogeneous equation of a damped harmonic oscillator in order to see how the error propagates. $$\frac{d^2 X}{d\phi^2} + ...
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Are Black Holes set to take over the Harmonic Oscillator in the 21st century?

A few years ago I attended a talk given by Andy Strominger entitled Black Holes- The Harmonic Oscillators of the 21st Century. This talk, ...
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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). ...
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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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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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756 views

Effective mass in Spring-with-mass/mass system

Suppose you have a particle of mass $m$ fixed to a spring of mass $m_0$ that, in turn, is fixed to some wall. I'm trying to calculate the effective mass $m'$ that appears in the law of motion of the ...
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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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WKB approximation in two dimensions

Does anybody know how to implement the WKB approximation for the two-dimensional Schrodinger equation with a harmonic oscillator potential: $\frac{1}{2}\Biggl[-\biggl(\frac{\partial^2}{\partial ...
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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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Different hamiltonians for quantum harmonic oscillator?

The Hamiltonian for a classical simple harmonic oscillator is $$ H = \frac{p^2}{2m} + \frac{1}{2}m\omega^2x^2$$ With the usual choice of the ladder operators $$a = ...
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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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Conservation of energy in a quantum harmonic oscillator after a sudden change in spring constant

At a given instant of time, a harmonic oscillator undergoes a sudden change in spring constant from $k$ to $k'$. Show that for energy to be conserved in the accompanying transition, $\sqrt{k/k'}$ must ...
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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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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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Quantum oscillator, position mean value problem

A quantum harmonic oscillator of mass $m$ and frequency $\omega$ is at time $t=0$ in the state: $$ \left|\psi(t)\right> = \sum_{n=N-\Delta N}^{N+\Delta N}\left|n\right>\frac{1}{\sqrt{2\Delta N ...
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Raising and lowering 3D harmonic oscillator state

A good solution to the 3D harmonic oscillator is shown here. This gives the basis states $|n,\ell\rangle$ My question is if there are some operators comparable to the 1D SHO that will raise either n ...
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Finding Tension in an Elastic String?

I know that this is a homework type question and I'm not asking a particular physics question, but I'm really desperate for help. Here's the question: I tried to divide the string to 2 parts with ...
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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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Is strictly harmonic 2D lattice made of Hooke springs possible?

If we connect a set of point masses in a 1D lattice with Hooke springs and consider longitudinal oscillations, we'll have a strictly harmonic system, for which there exist eigenmodes and the frequency ...
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A basic question about Heisenberg State Kets (in particular the simple harmonic oscillator)

I know base kets in the Heisenberg picture are $U^\dagger |{a}\rangle$ but if the base kets are the base of the hamiltonian, and the hamiltonian is independent of time, are all of the base kets ...
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Equations of motion for a pendulum and spring system

The question is available here: I've modeled the building as a rod on a torsional spring (with a pendulum hanging from the top). $\phi$ is the angle from the centre for the pendulum and $\theta$ ...
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Periodic sequence with exponentially increasing period?

I have to develop a physical model for a certain type of biological oscillation that can be built upon periodic sequences. From earlier questions I know that any periodic sequence (containing $0$s ...
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Delivered/Reflected Power by Drive on a Hamiltonian System

Imagine a SHO with a drive F(t). (or in general a Hamiltonian system) What is the power delivered to the system and can we talk about the power reflected? is i am imagining say a MW oscillator ...
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How can I model a polyatomic molecule as a system of coupled oscillators?

(Classical Mechanics) Let's say I have a polyatomic molecule, what is the best way for finding the equations of oscillations if they are bounded by a torsion spring?
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817 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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Finding the total space that an oscillating body has gone through via complex analysis

I was solving my homework and I got to an exercise that stated: An harmonic oscillating body has an equation of $$y(t) = A \sin(t)$$ Find the total space that the body has travelled during $t \in ...
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Nuclear Physics: Eigenvalues of nucleus angular moment

In the shell model of nuclei, when we talk about collective motions, we describe any nucleus deformation, expanding its radius on spherical harmonics base like this $R(\theta,\phi) = ...
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63 views

Calculation of energy eigenvalues of $\hat{x}^4$

I would appreciate help in calculating the energy eigenvalues associated with $\hat{x}^4$, with $\hat{x}$ expressed using the ladder operators for harmonic oscillators. $\hat{x} = ...
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damped and undamped oscillation graph comparison

I have been trying to solve a problem which compares the two motion. If the undamped free harmonic oscillator motion is $ x=A\sin\omega_{o}t$. So the corresponding motion in case of damped motion will ...
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Uncoupling a coupled oscillator Hamiltonian by change of variables

I'm working on the problem of two entangled harmonic oscillators with Hamiltonian: $$H = \frac{1}{2} [p_1^2 + p_2^2 + k_0(x_1^2 + x_2^2) + k_1(x_1 - x_2)^2].$$ Introducing the variables $x_± = ...
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Heisenberg picture usage - Merzbacher 14.106

I am trying to understand a line in the quantum mechanics book by Merzbacher, specifically the second line of equation 14.106. The problem is a forced quantum harmonic oscillator. The Hamiltonian ...
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Interesting Harmonic Oscillator Solution

On page 89 of Griffith's QM book, an exact solution to the time-dependent SE equation for the harmonic oscillator is mentioned: $$ ...
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In an oscillating system (SHM) with a constantly increasing amplitude, how do you relate the constant period with the highest amplitude

For example, I am working on this problem, and I don't know where to begin. All the relationships that I can think of include a constant amplitude. [A (w/w^2) sin/cos theta] Here's the problem: A ...
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Mass frequency problem

For Dispersion relation , according to Gaussian profile, the author in the equation 3 wrote as $\omega= \left(k^2+\omega_{mass}^2\right)^{1/2}$ My question is what is mass frequency and how it arose ...
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Finding an efficient strategy for walking

Let's say you are already walking at a maximally efficient combination of pace and stride (or $\omega$ and $X_0$ I guess) but you need to reach your destination faster. Should you increase/decrease ...