All Questions
Tagged with shm or harmonic-oscillator
2,480 questions
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Time translation invariance of the two-point function
Please refer to this 2023 lecture note by Douglas Ross. In this note, they compute the generating functional for the correlators given by Eq (4.7) for a harmonic oscillator action.
$$\begin{aligned}
&...
- 1,429
2
votes
0
answers
39
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Why initial conditions matter while interfering with ongoing SHM of a mass with electric charge and placed in electric field?
The question is related to the situation:
A body of mass M and charge q is connected to a spring of spring constant k. It is oscillating along x-direction about its equilibrium position, taken to be ...
- 21
0
votes
1
answer
88
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Approximation to the differential equation $\dfrac{d^2\psi}{d \xi^2} = \xi^2 \psi$ for large values of $\xi$
I'm interested in understanding the approximate solution for large values of $\xi$ (as $\xi \rightarrow \infty$) of the following differential equation
$$\dfrac{d^2\psi}{d \xi^2} = \xi^2 \psi$$
which ...
0
votes
0
answers
42
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Why is this case different from case of simple SHM? [closed]
The question in itself is easy but my doubt is
If we consider a block falling from top to an unstretched spring then it starts performing shm(if the block is connected to the spring). on the bottom ...
- 35
1
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0
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29
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How to measure the distribution of eigenenergies of a cold atomic cloud in an optical trap?
I have a cloud of cold atoms in an optical trap.
For example a BEC or thermal gas of 87Rb (you can adjust the number from 100 to 10^6) in a harmonic trap created by some far detuned laser.
You want to ...
- 207
0
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2
answers
46
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What sort of coupling of oscillators yields a potential of $\lambda q(t)Q(t)$?
I'm trying to work through Galley's paper, The classical mechanics of non-conservative systems. It starts with a toy problem to demonstrate the need for his full approach. I'm certain understanding ...
- 51.7k
-4
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1
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65
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Energy in simple harmonic oscillator in a moving frame of reference
It is pretty straightforward to derive the kinetic energy and the potential energy of a simple harmonic oscillator and to see that they behave like the squares of two sinusoids with a phase difference ...
0
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2
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91
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How to easily prove that operators in the Heisenberg picture have the same expression through other operators? [closed]
I was reading a textbook, and didn't understand this implication. Suppose we have a harmonic oscillator. We know that
$$
a_H = a_S e^{-i\omega t}, a_H^{\dagger} = a_S^{\dagger} e^{i\omega t}
$$
It ...
0
votes
2
answers
80
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Why is the form of the ladder operators for the QHO what it is?
I'm trying to deepen my understanding of the ladder operators for the quantum harmonic oscillator now that I'm further along in my physics degree, and I can't seem to find anything on why they take ...
- 85
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Why does the EBow work if an electromagnet will pull the string twice per period
I've been thinking about a similar yet not the same idea as the OP of this elderly thread. I don't know how to properly interact with that thread as a obviously do not have an answer nor am I allowed ...
0
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1
answer
72
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Two answers to one problem, but both seem correct (mathematically) [closed]
The question is:
Two particles are performing SHM along the $x$-axis and about the origin. If the maximum separation between them is equal to their amplitude $A$, find the phase difference.
Method 1-...
2
votes
3
answers
192
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Does $x(t) = a \sin^2(\omega t+c)$ represent a Simple Harmonic Motion or not?
I had a doubt about the equation
$$x(t) = a \sin^2(\omega t+c).$$
Does this equation represent a Simple Harmonic Motion or not?
I did try it myself with 2 methods:
using trigonometry
using the ...
- 67
7
votes
1
answer
301
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What is the criterion for oscillatory motion?
A ball bouncing (consider ideal elastic collisions) moves to and from about some point, but there is no equilibrium position. This motion sure is periodic... but is it oscillatory?
What is the ...
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1
answer
64
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Understanding Quantum Harmonic Oscillator with Piecewise Potential [duplicate]
I just got out of an exam today, and have been wrestling with one of the questions.
I was given a simple (quantum) 1D harmonic oscillator, with potential given by:
$${V(x)=\infty, \forall x<0}$$
$$...
1
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0
answers
52
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Equations of motion for n-coupled pendulum system
With reference to this article (https://drive.google.com/drive/u/0/mobile/folders/1d-IF8FTyizKHbaHXjVSxfaB3bgciqi4p),
the author uses 2n equations, where n is the number of pendulums, to describe the ...
- 56
2
votes
1
answer
148
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IMAT 2024 question about a moving pendulum seems to be wrong [closed]
Here is the question from IMAT 2024:
A pendulum rod moves from the vertical position. Which of the
following statements is false?
A) In the absence of friction, the
pendulum tends to come to a stop ...
- 121
3
votes
3
answers
211
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What actually causes damping in a damped SHM? [duplicate]
We know and have been taught that due to friction on the surface of maybe a spring mass system, the body faces damping. But what is bothering me, is the fact that force due to damping is proportional ...
0
votes
1
answer
58
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Physical interpretation and validity of QHO hamiltonian term: $\hat{a}\hat{n} + \hat{n}\hat{a}^{\dagger}$ [closed]
For a quantum harmonic oscillator can we have a Hamiltonian term of the following form, and what would be its physical interpretation:
$$\hat{a}\hat{n} + \hat{n}\hat{a}^{\dagger}$$
1
vote
1
answer
56
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Reduced mass in a Harmonic Oscillator [closed]
I recently came across the harmonic oscillator and the concept of reduced mass, i.e
$$
\mu = \frac{m_1m_2}{m_1 + m_2}
$$
To begin, I understand the derivation from the point of view of sitting on one ...
- 13
0
votes
0
answers
40
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Fock Darwin wavefunction
The ground state of a 2D harmonic oscillator in magnetic field is a Gaussian wavepackets, and the spectrum of the Hamiltonian is solved by the Fock-Darwin states.
Are there textbooks (I want textbooks,...
0
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0
answers
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Tenth (even) harmonic of a open-closed tube
Can I say that a frequency (let's say f1) is the "tenth harmonic" of an open-closed tube?
I would say it does not because closed tubes only have odd harmonics, is that correct??I want to ...
2
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0
answers
74
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Volume element in QFT
The Hamiltonian of a free scalar field in QFT is given by:
$$\hat{H} = \int{\frac{\mathrm{d}^3k}{8\pi^3}\hbar\omega_k\left(\hat{n}_k + 4\pi^3\delta^{(3)}(0)\right)}.$$
And $\hat{n}_k = \hat{a}^\...
- 751
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1
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Confused in David Bohm's *Quantum Theory*
In discussing matrix mechanics Bohm says in chapter 16 of Quantum Theory that the $rm$ element of operator $A$, $a_{rm}$, is given by
$$a_{rm} = \int dx\ \psi^*_r(x)A\psi_m(x) \hspace{1in} (Eqn. ...
- 873
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0
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50
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Can all solutions from any possible dynamical systems be formulated as combinations of harmonic oscillators?
In my understanding, all physical oscillators are unit vectors of a Hilbert space that is represented from the group $SU(3)\times SU(2)\times U(1)$. Every dynamical system operates under this group (...
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0
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74
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Coherent state of a quantum harmonic oscillator [closed]
Let's consider a coherent state for a QHO which we denote as $\psi_{\lambda}(x,t)$.
While one can derive the appropriate expression for the coherent state, what I am interested in is a commentary made ...
- 1,624
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1
answer
80
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The eigenvalues of quantum harmonic oscillator [closed]
Can someone explain to me what is the green curve in the graphical rapresentation of energy levels for a quantum harmonic oscillator? I've always encounter this type of photo and nobody explains what ...
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1
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1
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63
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Expectation value of position in first-order perturbation [closed]
Suppose I have a simple harmonic oscillator in ground state and a time-dependent perturbation $V(t)=f(t) \hat{x}$ that turns on at $t=0$. How do I find the expectation value of position in t goes to ...
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2
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Proving the Plane Harmonic Oscillator move in an ellipse
My problems states that we have $r(t)$ satisfying $m\ddot{r}(t)=-kr(t)$
And in the first section we were asked to evaluate the derivative of $r(t)\times \dot{r}(t)$
And by cross product derivative law ...
- 145
2
votes
1
answer
81
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Gauge choice in showing Landau level degeneracy via the algebraic method
I'm trying to understand the algebraic method of formulating the Landau level problem better. I'm referring to David Tong's notes on the Quantum Hall effect for this (but not exactly following his ...
0
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1
answer
61
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It's more like a simple math question but how does this process to that? [closed]
I tried to adjust the equation multiple times to make it look like the second one, but I kept failing. Can someone please let me know how?
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1
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2
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120
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Which symmetries lead to the ladder operators of the harmonic oscillator?
It seems like symmetries usually lead to ladder operators. For example in a central potential problems the conservation of angular momentum leads to angular momentum ladder operators being used in the ...
- 441
1
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1
answer
90
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Selection rule in three dimensional harmonic oscillator in representation $(n,l,m)$
Selection rule for transition probability of first order perturbation . I don't understand why the selection rule $$\langle l'm'n'|x|l,m,n \rangle =\delta_{m'm} \delta_{n'n} \langle l'|x|l \rangle$$ ...
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1
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1
answer
56
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How Does Frequency Change With Damping (Underdamped Harmonic Oscillators) [closed]
I'm studying harmonic oscillators and I'm trying to model a system where both the frequency and amplitude decay over time. This is throwing me off because frequency decay is much less intuitive than ...
6
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6
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907
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How can I interpret the normal modes of this mechanical system?
How can I interpret the normal modes of this mechanical system?
The equations of motion for the system are as follows:
$$\left[\begin{array}{ccc}
m_{1}\\
& m_{2}\\
& & 0
\end{array}\...
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-2
votes
1
answer
50
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The period of simple harmonic motion [closed]
Am i understanding this correctly?
The harmonic oscillation of an object can be seen as the movement in the y direction along a circular path. So the time for one revolution around the circle will be ...
0
votes
1
answer
57
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What happens to the amplitude when a spring is compressed?
Say there's a spring lying on a horizontal table, with one end attached to a wall (say the left end) and it is in it's natural length. Now I compress the spring from the right end, and leave it. So ...
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0
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Why Is There No Oscillator Representation for Operators in Planar ${\cal N}=4$ SYM Theory?
I'm studying the planar ${\cal N}=4$ Super Yang-Mills (SYM) theory and I'm curious about the representations of its operators, specifically the Hamiltonian and the dilatation operator. In many quantum ...
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0
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1
answer
257
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Action-angle variables for three-dimensional harmonic oscillator using cylindrical coordinates
I am solving problem 19 of ch 10 of Goldstein mechanics. The problem is:
A three-dimensional harmonic oscillator has the force constant k1 in the x- and y- directions and k3 in the z-direction. Using ...
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2
answers
144
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When is minimum potential energy in simple harmonic motion not zero?
We know that in simple harmonic motion, potential energy is minimum at the mean position and it is zero since displacement is zero. So what are some cases in which minimum potential energy is not zero?...
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69
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Article on 1D deformed quantum harmonic oscillator
Few years ago I was reading an article which I'm trying to find for quite some time but with no success so far. It was a paper about deformation of 1D quantum harmonic oscillator with continuous ...
0
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1
answer
142
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How is the quantum harmonic oscillator related to Fock states?
The question is basically in the title.
From what I understand, in the Fock state there is a certain number of particles in each energy level. The creation/annihilation operators create or destroy a ...
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1
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If friction is not proportional to velocity, why do we model it as such when considering damped oscillations? [duplicate]
Early in our study of mechanics, we learn that friction is usually proportional only to normal force, without dependence on velocity. However, during our studies of damped oscillations, we often model ...
0
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2
answers
46
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Why am I getting this derivation of time period of pendulum in an accelerated frame wrong? [closed]
We are working in the frame of the cart and we are trying to obtain the $\tau=k\theta$ form.
So, let's write the $\tau=I_{axis}\alpha$ first for a small deviation $\theta$ from the vartical.
(The ...
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1
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1
answer
68
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Potentials increasing faster than harmonic oscillator
I'm reading a book which says: (HO stands for harmonic oscillator):
The spectrum of the HO has equidistant energy eigenvalues. A potential that increases quicker than the HO has states which become ...
- 379
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1
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50
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Spherical quantum oscillator: Is energy smaller than the potential?
A particle with mass $m$ is inside the spherical quantum well $V(r)$:
\begin{equation}
V(r)=
\begin{cases}
-V_0, & \text{if}\ r<a \\
0, & \text{otherwise}
\end{cases} \...
- 109
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0
answers
44
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Understanding the dynamics of a perturbed quantum harmonic oscillator system
I'm trying to understand how quantum systems behave when they are perturbed, and I'm using the quantum harmonic oscillator as a model.
I start by implementing a symmetric gaussian shaped bump in the ...
- 21
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3
answers
65
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Investigation Results of Damping of A Spring Showing Changing Phase Angle? Why?
In an experiment I've recorded the displacement of the spring over time, investigating underdamped simple harmonic motion.
Using pre-existing formulae the data should conform to a curve of the form
$$...
1
vote
2
answers
60
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Infrared regularizing the harmonic oscillator path integral
This is from Laine and Vuorinen’s Basics of Thermal Field Theory. I do not understand why the fact that the integral over $x(\tau)$ implies the following regularization scheme. That is, I don’t ...
- 11
1
vote
0
answers
43
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Oscillating body and Doppler effect
Say we have a body attached to a spring, oscillating with some frequency $\nu$. This is one of the simplest problems studied in elementary Physics, and yet I've noticed we always study it positioning ...
- 1,870
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votes
1
answer
104
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Regarding to the asymptotic solution of quantum harmonic oscillator
In quantum mechanics, the radial equation of the SHO takes the form
\begin{align}
\frac{d^2 u}{dx^2}+\left(\epsilon-x^2-\frac{l(l+1)}{x^2}\right)u=0,
\end{align}
where $x=\sqrt{\frac{m\omega}{\hbar}}r$...
- 27