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.
154
questions
2
votes
1
answer
86
views
Probability distribution for the momentum of a quantum harmonic oscillator
I was wondering if anyone could point me towards the analytical solution for the probability distribution for the momentum of a quantum harmonic oscillator in the canonical ensemble. I've come across ...
- 121
1
vote
1
answer
126
views
Are the SHO's ladder operators induced from a Lie group action?
Consider a quantum system with a hamiltonian $\hat{H}$, which is invariant under the action of a lie group $G$, meaning we have a unitary representation of $G$, $\hat{U}(g)$, in Hilbert space, and $\...
- 812
6
votes
2
answers
261
views
Energy levels of a translating quantum harmonic oscillator
It is well known that the energy levels
$$
E_n = \hbar \omega\left(n+\frac{1}{2}\right)
$$
of the quantum harmonic oscillator verify the eigenvalue problem
$$
\hat{H}|\psi_n\rangle = E_n |\psi_n \...
- 1,232
0
votes
0
answers
48
views
Question about a harmonic oscillator
I was solving the following problem on harmonic oscillation and I don't understand a specific part in the proof. I will emphasize (italic) the part which I don't understand.
Problem:
The following ...
- 101
0
votes
1
answer
33
views
The time-derivative of the Hamiltonian for a 1D harmonic potential [closed]
I do not understand how to take the time derivative of the following Hamiltonian $\hat{H}(t) = \frac{\hat{p}^2}{2m} + \frac{1}{2}m\omega^2(\hat{x}-a(t))^2$, where $a(t) = v_0t$. For instance how does ...
- 3
1
vote
2
answers
66
views
Coherent creation operator: unitary or not?
In Quantum Mechanics, for coherent states $|z\rangle$ it can be prooved that if $|0\rangle$ is the vacuum state for an harmonic oscillator, therefore:
\begin{equation}
|z\rangle=e^{za^{\dagger}-z^*a}|...
2
votes
2
answers
70
views
Why is time period same even if you give an impulse perpendicular to the spring?
It all started with this question.
There are three different ways to solve this but one way is using kepler's second law. $\frac{dA}{dt}=\frac{L}{2m}.$ This applies because angular momentum is ...
- 45
1
vote
2
answers
48
views
Period of the pendulum (realistic) is shortening in time?
I am doing an experiment with a pendulum and am trying to measure its period over time. I built myself a contraption that uses a 3D printed pendulum with a weight attached at the end.
For this ...
0
votes
1
answer
84
views
What really is oscillatory motion in physics? [duplicate]
Is it that oscillatory motion must be to-and-fro motion about a mean/stable equilibrium position, or it does not qualify as true oscillatory motion? Or, is it that most of the oscillatory motion has a ...
2
votes
2
answers
143
views
Is bouncing ball (100% collision) an oscillatory motion/SHM or both or none?
My teacher told me bouncing ball (100% elastic) is oscillatory motion that does not have a stable equilibrium position and restoring force. It is just to and fro motion and thus called oscillatory ...
1
vote
3
answers
215
views
Damped Quantum Harmonic Oscillator with sinusoidal driving force
The standard Damped one-dimensional Harmonic Oscillator with sinusoidal driving force has equation
$$\frac{d^2}{dt^2}x(t)+2\zeta\omega_0\frac{d}{dt}x(t)+\omega_0^2x(t)=\frac{1}{m}F_0\sin(\omega t).$$
...
- 1,440
0
votes
2
answers
47
views
Quantum position in molecular vibration
Evere molecule consists of atoms that vibrate around their equilibrium positions. This can be viewed from a classical or a quantum perspective. However, I found a seeming inconsistency between these ...
- 1,440
0
votes
1
answer
31
views
If a damped mass-spring oscillator is equivalent to a resonant bandpass filter, then in audio signal terms, what is the input signal for both?
Background
I am working on some personal audio processing and synthesis experiments in the sample domain. I posted here about how a resonant bandpass filter with a given $Q$ and frequency $f_0$ is ...
- 321
2
votes
1
answer
37
views
How do the amplitudes of longitudinal wave harmonics in a string vary with excitation (pluck) position?
A very good explanation for the amplitudes expected for each harmonic of an ideal string with a transverse excitation is included here.
The final equation given is:
$$b_n = \frac{2AL^2}{\pi^2\ell(L-\...
- 321
2
votes
4
answers
765
views
Why is Simple Pendulum not SHM?
Why does Simple pendulum's motion not hold as SHM for large angles, only for small angle approximations? The restoring force is still directed towards the mean position. I know mathematically the ...
