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
0
votes
2
answers
88
views
Ladder operators and creation & annihilation operators - different between $a$, $b$ and $c$ [closed]
Usually, the ladder operator denoted by $a$ and $a^\dagger$. In some case, people talk about the creation operator and denote it by $c$ and $c^\dagger$. Recently I see another notation, $b$ and $b^\...
- 23
2
votes
0
answers
34
views
The interpretation of the Bose occupation factor
I was reading into the Oxford solid state basics, by Steven H.Simon and I stumbled upon a confusing interpretation of the Bose Occupation factor: $$n_B (x) = \frac{1}{e^x-1}$$ with: $$x = \beta \hbar \...
- 41
0
votes
1
answer
63
views
Doubt obtaining the expected value of $x^2$ of a bidimensional harmonic oscillator
Just for the sake of context I'll add a little bit of introductory of the theory we were doing:
Say we are in the context of a bidimensional isotropic harmonic oscillator with an energy found of $2\...
- 75
2
votes
1
answer
46
views
Plot of Number of Oscillations of a Pendulum
I have been studying the oscillations of a ball attached to a string which is released from some initial angle $\theta$. The number of complete oscillations over a certain time interval $\Delta t$ is ...
- 1,410
-1
votes
3
answers
87
views
Can we equate SHM with motion in a circle?
So in SHM, $v = r\omega\cos\omega t$. But we also know that $v = r\omega$ from circular motion. Then, we can write
$$r\omega = r\omega\cos \omega t$$
$$1 = \cos\omega t \tag{1} \label{1}$$
$$0 = \...
0
votes
0
answers
44
views
Ground state of an harmonic chain and Klein-Gordon vacuum
Consider the lagrangian of a system of classical coupled harmonic oscillators of mass $M$, connected with springs with elastic constant $\chi$ and connected to the background with springs of elastic ...
0
votes
1
answer
43
views
What is the equation if that projection starts SHM on the $x$-axis from extreme position?
Consider A particle performing Uniform Circular Motion.
We know that its projection on diameter performs SHM.
Then, if that projection starts SHM on the y axis from mean position, then $y=A\text{sin}(...
- 11
1
vote
2
answers
82
views
Does it make sense to talk about individual energies of interacting quantum particles?
Does it make any sense to talk about energy of any one particle in an interacting system? For example if we talk about a system of two coupled quantum harmonic oscillators of same mass and frequency, ...
0
votes
2
answers
57
views
Does the motion of a simple pendulum shifts to SHM, due to damping?
I have doubt in damping oscillations of a pendulum. Let's consider a simple pendulum in a drag medium like air. Suppose if the angular displacement (theta) is larger (say 40°), the oscillations start ...
- 43
7
votes
1
answer
204
views
How to get the factor of $n^{-27/4}$ in number of open string states from the calculation in GSW's book?
In section 2.3.5 of Green, Schwarz, Witten's book on string theory (volume-1) pp. 116-118, the objective is to calculate an Asymptotic Formula for Level Densities $d_n$ for open bosonic string theory. ...
- 785
2
votes
0
answers
66
views
How to solve the coupled equation of motion? [closed]
there we have the EOM:
\begin{align*}
\alpha q_{2} + \lambda - \ddot{q}_1=0 \\
\alpha q_{1} + \lambda - \ddot{q}_2=0
\end{align*}
and $q_{i}$ is the canonical coordinates. Can I use the Fourier ...
- 49
0
votes
1
answer
53
views
Eigenvalues and Normal Modes in SHM
I'm reading Symmetries part from the textbook provided by MIT OCW Physics3 8.03SC course, but have a question about the condition to find normal modes of SHM. In the book they mentioned
$S$ - symmetry ...
- 3
0
votes
1
answer
58
views
What defines weightlessness feeling during a fall?
So I know that we feel weightless during a free fall as there's no normal force acting on us or my other way of thinking is that considering a lift and both lift and I fall with $g$ then no normal ...
- 91
0
votes
1
answer
51
views
Planck's quantum explanation of black body radiators
Oscillators in a black body (electrons) can only have energy equal to $E = nhf$ ie it is a linear relationship. so if an electron drops from energy level $n$ to a lower energy (jumping 1, 2,3 ... ...
- 13
0
votes
0
answers
90
views
Classification of equilibrium configurations for particles subject to elastic force constrained on a circle
I am interested in classifying all the possible equilibrium configurations for an arrangement of $l$ equal point particles $P_1, P_2, . . . , P_l$ $(l > 2)$ on a circle of radius $R$ and centre $O$....
- 130