Tagged Questions

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.

105 views

Is it possible to derive the angular frequency of a simple harmonic oscillator using total energy?

I want to show that $$\omega=\sqrt{\frac{k}{m}}$$ using the fact that $$E=K+U=\frac{1}{2}mv_x^2+\frac{1}{2}kx^2=\frac{1}{2}kA^2.$$ The issue is that I have derived a formula that isn't ...
130 views

Using creation and annihilation operators to prove the expression for the $n$th excited state in terms of the vacuum state

How does one prove that the $n^{th}$ excited state of a quantum harmonic oscillator (QHO) can be obtained by applying the creation operator $a^{\dagger}$ $n$-times to the vacuum state $\vert 0\rangle$?...
138 views

Has anyone published the procedure to generalize ladder operators for any potential in Schrodinger's equation?

I know that the ladder operator for the quantum harmonic oscillator \begin{align} H\psi_m = \left(\dfrac{p^2}{2m}+\dfrac{1}{2}m\omega^2x^2\right)\psi_m=E_m\psi_m \end{align} is \begin{align} A = \sqrt{...
80 views

Can an object experience torque when the only applied external force is at its axis of rotation (IOW, where $F \times r = 0$)?

This question came up because of this diagram that I saw in my textbook of an angular simple harmonic oscillator. I've always struggled a bit with torque and rotational dynamics in general, and I ...
609 views

97 views

How to calculate the resultant movement of a superposition of harmonic oscillators?

If $x_{1}(t) = \cos(\omega t - \frac{\pi}{6})$ and $x_{2}(t) = \sin(\omega t)$ are two simple harmonic oscillators in the same direction and with the same angular frequency $\omega$, how to calculate ...
54 views

556 views

The universality of the Stuart-Landau equation to describe nonlinear oscillators

I have read numerous papers which boldly suggest that the Stuart-Landau equation can be successfully used to model any weakly nonlinear oscillating system near a Hopf bifurcation. Even thought it has ...
241 views

Can vertical SHM occur in a system of a mass between 2 springs between 2 vertical pillars? [closed]

The problem is detailed above. I have worked through problems involving SHM in the horizontal plane, but unsure how to go about it vertically. I know the weight component would need to be incorporated....
148 views

A pendulum in an elevator - looking upside down

If I have a pendulum connected to the floor of an elevator by a string, and the elevator is falling in an acceleration greater than g - can I just "rotate" the system and look at it as a regular ...
169 views

Harmonic oscillator problem - Griffiths [closed]

I'm solving problems about harmonic oscillator from Griffiths book (2nd ed.) and I'm stuck in the problem 2.13. When I normalize the equation 2.51 to get $A_1$ my final wave function is complex, since ...
75 views

Why in analysis of coupled oscillator, restoring force for uncoupled condition is taken in account?

If the pendulums were free & either one were displaced a small distance $x$, the restoring force would be $m{\omega_0}^2 x$. But in the present situation the coupling spring is stretched a ...
So, short and sweet, I've been reading the path integrals book by Feynman and Hibbs, and one of the elementary problems they ask is to calculate the classical on-shell$^1$ action of a harmonic ...