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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Wave Function for a Sinusoidal Wave (Why minus sign?)

I was trying to understand how the wave function for a sinusoidal wave was derived, but did not understand one specific sign, the minus sign in the following formula: $$y(x,t) = A \sin(k x – \omega t ...
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How to find zero-point oscillations for this system?

Consider the following Hamiltonian which is absolutely relativistic literally: only sensitive to absolute pairwise relative phase space variables of objects for a system of $N$ objects moving in one ...
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Using $\sin()$ or $\cos()$ for computing SHM?

In simple harmonic motion, you can use either the sin or cos form of the equation but my question is which one do you use when and why? I am having a tough time understanding this, so any help would ...
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Frequency of kinetic energy in shm

I am currently learning about simple harmonic motion. In a book I am reading it says frequency of kinetic energy is twice the frequency of velocity for a harmonic oscillator by showing velocity vs ...
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Why do electromagnetic waves oscillate?

I've been considering this question, and found many people asking the same (or something similar) online, but none of the answers seemed to address the core point or at least I wasn't able to make ...
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1answer
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Change of operator in the Hamiltonian [closed]

We are told that the particle has mass m and charge e and is moving in 2 dimensions. The position operator $\mathbf{X}=(X_{1},X_{2})$ and momentum operator $\mathbf{P}=(P_{1},P_{2})$ We are given ...
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Harmonic oscillator

Let $|0\rangle,...$ be the states of the harmonic oscillator. Then a squeezed state was defined as $|\xi\rangle =S(\xi)|0\rangle $, where $S(\xi):=e^{\frac{1}{2}( \xi (a^{ \dagger ^2}-a^2))}$, where ...
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57 views

Angular momentum of anistropic harmonic oscilator

A potential given by : $$ V(x,y,z) = \frac{1}{2}m(x^2+y^2+\frac{z^2}{2}). $$ Which component of angular momentum is conserved. An attempt: Angular momentum along z, $ L_{z} = m(x\dot{y} - ...
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Harmonic oscillator modified by infinite well: are analytic solutions possible?

I'm trying to find solutions to a harmonic oscillator that sits within an infinite square well. I haven't spent too much time yet, and I've had no success so far. I'm wondering how possible or complex ...
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Why is a coherent state an eigenfunction to the annihilation operator? [duplicate]

In class when we talked about the harmonic oscillator in QM we noticed that the eigenfunctions to the annihilation operator are coherent states in the sense that they have minimum uncertainty in ...
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2answers
630 views

Velocity and acceleration in SHM

Can velocity and acceleration reach maximal values during the SHM simultaneously? Can you explain why?
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1answer
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Spring problem? [closed]

I came across this problem in physics "Physics for Scientists and Engineers with Modern Physics by Serway" A block on the end of a spring is pulled to position $x = A$ and released from rest. In ...
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1answer
668 views

Three-mass, two springs copled oscillator NOT attached to walls

Int he three-mass coupled oscillator problem, we often see it stated that you have three masses, (they can be equal or not, but we'll assume they are equal here) connected by two springs and then ...
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Complex Fourier Particular Solution [closed]

I have found the complex Fourier series for my desired force. I now need to find the steady-state forced vibration of my oscillator as a Fourier Series. (The particular solution to the inhomogeneous ...
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1answer
449 views

Isotropic harmonic oscillator in polar versus cartesian

I read another Phys.SE post here: 3D Quantum harmonic oscillator that I believe says the wave function in Cartesian coordinates for a 3D harmonic oscillator is the product of the 3 one dimensional ...
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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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1answer
363 views

Simple pendulum. quick question [closed]

I was trying to find an equation to find $T$ and $\omega$ for a simple pendulum when in an elevator while the elevator is accelerating. One scenario is when it accelerates in the positive up ...
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1answer
21k views

How to find the phase constant? [closed]

I was given this velocity-vs-time graph of a particle in simple harmonic motion: I determined the amplitude to be $A = 1.15$ m, which Mastering Physics confirmed is correct. Then I was asked to ...
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1answer
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Equations of motion for a pendulum in 3D?

I am trying to solve for the equations of motion to simulate a pendulum. I decided to use the spherical coordinates. The Lagrange equation is: where L = length of the rope ϕ= angle of the ...
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1answer
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Ground State Wavefunction of Two Particles in a Harmonic Oscillator Potential

Question: Two identical, non-interacting spin-$1/2$ particles are in a 1D Harmonic Oscillator Potential. Their Hamiltonian is given by ...
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Eigenfrequencies of Normal Modes

I understand the whole deal with coupled oscillators and how to solve for normal modes and eigenfrequencies and such. But what is tripping me up is what these eigenfrequencies correspond to. If I ...
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1answer
597 views

What is the correct Hamiltonian for a system of coupled quantum oscillators?

The Hamiltonian (see Eqn. 1 in Appendix 2 of this paper) for a system of coupled quantum oscillators is given as $$H=\frac{1}{2}∑_{i}p^{2}_{i}+\frac{1}{2}∑_{j,k}A_{jk}q_{i}q_{k}$$ Yet, in my QM ...
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431 views

Period of small oscillations [duplicate]

A light elastic string is stretched between two points, one lying vertically below the other. A particle is attached to the mid-point of the string, causing it to sink a distance h. Assuming that ...
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1answer
407 views

Harmonic Oscillator Expectation Value

In Calculating the expectation value of the quantum harmonic oscillator, I've come across a problem for finding $\left \langle x \right \rangle$ for the coherent state $\left| \alpha \right \rangle$ ...
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Mass-spring system on an incline

I am reviewing for an exam next week, and this is one of the questions I am stuck on. I have the mass-spring system above with spring constant $k$ on a frictionless incline. I would like to find the ...
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1answer
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General way to model baths? Harmonic Oscillators valid?

I am trying to model an open system interaction without making strong assumptions on coupling strength or temperature. In general i understand that open systems are modeled by a Lindbladian, but as ...
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738 views

The harmonic oscillator - ladder operators

Reading from Griffiths. I have got two questions. First, the halmiltonian operator that used to find the energy eigenvalue in only harmonic oscillator is: $$H={\hbar}w(a_-a_+-\frac{1}{2})$$ and ...
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5answers
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Is $\langle\psi_1|p\psi_1\rangle$ necessarily 0 for eigenstates? [closed]

Is $\langle\psi_1|p\psi_1\rangle$ necessarily 0 for harmonic oscillator eigenstates? If $\Psi(x,t)= c_0\psi_0(x)e^{-iE_0t/\hbar}+c_1\psi_1(x)e^{-iE_1t/\hbar}$, is the following true? Where $p$ is ...
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Harmonic Motion [closed]

A light elastic string is stretched between two points, one lying vertically below the other. A particle is attached to the midpoint of the string, causing it to sink a distance h. Assuming that the ...
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3answers
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Why Don't the Ladder Operators Commute?

I have two problems with ladder operators. The first is that I feel they should somehow result in measurable things. The asymmetry of applying the plus operator versus the minus operator is very ...
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2answers
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How To Use Ladder Operators?

I'm studying for a test in quantum mechanics and I'm having a hard time understanding how to use ladder operators. There are no examples in my text book, only definitions that I can't understand how ...
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1answer
536 views

Determining the spring constant in an oscillation problem [closed]

A 130g air-track glider is attached to a spring. The glider is pushed in 10.4cm and released. A student with a stopwatch finds that 14.0 oscillations take 19.0s I would like to know why the ...
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1answer
118 views

Interpretation of Free Damped Vibrations

I'm studying vibrations; so I'm using Beer-Johnston-Cornwell Dynamics book. I am worry about the equation for Underdamped Vibration, which in the book it is: $$x_{(t)}=x_0e^{-\lambda ...
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LC Oscillator and relativity

There are two identical LC oscillators with electronic counters attached indicating how many times they have oscillated (from the time they are turned on). They are turned on simultaneously and one is ...
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1answer
77 views

Infinite period in Simple Harmonic Motion

I'm studying the Simple Harmonic Motion, and I am hesitant about, how to get mass values for infinite period? When mass is 0. When mass is infinite. With $\tau=2\pi/\sqrt{k/m}$.
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1answer
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Harmonic Oscillator (Quantum Mechanics)

Griffiths uses an algebraic "brute force" technique to solve the harmonic oscillator. I'm somewhat confused regarding a few parts. $$\frac{1}{2m}[p^2 + (m \omega x)^2] \psi = E \psi$$ $H = ...
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513 views

Two-block system connected to a spring

Say you have two blocks with masses $m_1$ and $m_2$, where $m_1>m_2$. The smaller block sits atop the larger block. The larger block is connected to a spring, which is then connected to a wall a ...
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1answer
363 views

Quantum harmonic Oscillator analytic method

I'm using a book from Griffiths, I got really stuck about how he arrived at the approximate solution, is it just by trying( trial solution method?), I really appreciate any help on this. ...
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1answer
208 views

Finding the tangential force experienced by a bob of mass m on a simple pendulum via the gradient/nabla operator)

The problem was posed as follows. Given a pendulum of length $L$ with a mass $m$ attached to it, which forms an angle $\theta$ from the y-axis to the direction of swinging. First we had to find the ...
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1answer
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Spring with changing equilibrium

Suppose that we have two cars on a track, each with a different mass. Now suppose that the cars are connected with a spring. We smack one car. I would like to write down the equations of motion for ...
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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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Average Energy of the Quantum Harmonic Oscillator

In Griffiths, the average potential energy for the quantum harmonic oscillator is given as $$\langle V\rangle~=~\frac{1}{2}\hbar \omega(n+\frac{1}{2}).$$ Is the potential energy of the quantum ...
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1answer
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Expectation value of total energy for the quantum harmonic oscillator [closed]

A particles unnormalized wavefunction is given as $$\psi(x)=2\psi_1+\psi_2+2\psi_3.$$ How can I find $\langle E\rangle $ without calculating $\langle T\rangle$ or $\langle V\rangle $ ...
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Simple harmonic oscillator: zero point energy?

Today we had a lecture on the simple harmonic oscillator and its quantum mechanical treatment. My teacher derived the equation for it and finally concluded it has some zero point energy. My ...
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2answers
226 views

“Complex Variables Method” in Diff. Eq. - Justification and physical meaning?

A common method of simplifying calculations that involve differential equations - particularly involving oscillation - is to replace $\cos(\theta)$ with $e^{i \omega t}$, evaluate, and then take the ...
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2answers
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Vibration of pulley and string system [closed]

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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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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1answer
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Equations of motion for a spherical pendulum in a non-inertial reference frame

Take a spherical pendulum with bob mass $m$, rod length $\ell$ and physical coordinates $\theta$, $\phi$ (spherical angles) and $h$ (the hinge height with respect to the coordinate origin). The rod is ...
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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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1answer
412 views

Coupled Oscillators

This is an exercise of my last exam. Since I couldn't find anybody who solved it or knows how to, it would be really nice if somebody could tell me if my thoughts on it go into the right direction. ...