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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Is it true that spring has more force acting on it at its positive maximum amplitude than than at the negative one?

Am I missing something? It seems obvious to me that at $+A$ and $-A$, the spring has restorative forces equal in magnitude but opposite in direction. But since gravity is always pulling it down, ...
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1answer
39 views

Is harmonic oscillator continuous variable system?

In the literature I have seen that the notions "our system is continuous variable system", "Hilbert space of our system is infinite" were used as if they were equivalent. For example for harmonic ...
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1answer
50 views

Can you help me with physics homework please? [closed]

An object with a mass M is suspended from an elastic spring with a spring constant k. The object oscillates with period T on the surface of Earth. If the oscillating system is moved to the ...
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0answers
18 views

Is the electron-hole pair a 1D quantum oscillator or 3D oscillator

I'm trying to use fluctuation dissipation theorem to describe spontaneous photon emission process by electron-hole recombination in semiconductor material. I notice that all the references using such ...
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0answers
11 views

Is there an analog to the Runge-Lenz vector for a harmonic potential?

The Runge-Lenz vector is an "extra" conserved quantity for Keplerian $\frac{1}{r}$ potentials, which is in addition to the usual energy and angular momentum conservation present in all central force ...
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73 views

Free energy of coupled classical harmonic oscillators

I'm looking to find the thermodynamic (NVT) free energy of a classical coupled harmonic oscillator system such as the one below: (image taken from ...
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1answer
58 views

Eigenstates of sum of creation and annihilation operators

Does the operator $a+a^\dagger$ have eigenstates? If yes, what are they?
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1answer
48 views

Derive frequency given potential using Newton's laws

A mass with mass $m$ has a potential energy function $U(x)$ and I'm wondering how you would find the frequency of small oscillations about equilibrium points using Newton's laws. I started by finding ...
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2answers
132 views

Simple Harmonic Motion in Special Relativity

I was trying to see what results I would get if I were to incorporate relativistic corrections into the case of a harmonic oscillator in one dimension. I thought that if the maximum velocity of the ...
4
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2answers
83 views

Hamiltonian related to Riemann zeta function [closed]

using the eigenvstates of the Harmonic oscillator could we give a meaning to the Hamiltonian $$ H=\log(a.a^{+}+1) $$ here $ a$ and $ a^{+}$ are the creation/anihilation operators with commutation ...
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0answers
76 views

Creating an arbitrary state of the quantum simple harmonic oscillator

Suppose $\mathcal{B}=\{|0\rangle, |1\rangle, |2\rangle, ... \}$ is the energy eigen-basis of a quantum simple harmonic oscillator. I want to create the state \begin{equation} |\Psi\rangle = ...
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1answer
61 views

Finding the wave function of a quantum harmonic oscillator [duplicate]

How can I find the wave function of a quantum harmonic oscillator? If I measure its energy several times, my measurements will change the state of a system. All I know are the possible states, given ...
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0answers
30 views

The classical correspondence in the harmonic oscillator

In the harmonic oscillator, the ground state is the one with minimum uncertainty (and also other squeezed states that satisfy the 'equal to' in the Heisenberg inequality). This should mean that these ...
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1answer
28 views

Undamped Resonance of a Classical Harmonic Oscillator

Consider an undamped harmonic oscillator. It may be driven at it's natural frequency, $\omega_0^2 = \frac{k}{m}$. According to Feynman, and other sources, were this to happen, the amplitude of the ...
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1answer
34 views

Creation and annhilation operator in the Heisenberg picture

I am trying to calculate the time evolution of the creation/anni. operator in the Heisenber picture. On this webpage http://quantummechanics.ucsd.edu/ph130a/130_notes/node191.html, they used the ...
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1answer
48 views

General solution of a mass spring system

This is the differential equation that describes small amplitude vertical oscillations of a mass $m$ that is hanging from a spring $$\frac{d^2x}{d t^{2}} + \frac{b}{m}\frac{dx}{dt} + \frac{k}{m} x = ...
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0answers
32 views

Oscillation frequency of a dipole

So I have found the potential to be: $U(x) = \frac{\mu_0 m_2 m}{4 \pi} (\frac{1}{(d+x)^3}+\frac{1}{(d-x)^3})$ Afterwards I have found the position which minimized the energy to be $x=0$. (By doing ...
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2answers
68 views

What is the physical reason that the undamped driven oscillator has mean power zero?

The instantaneous power absorbed by an undamped driven oscillator is given by:$$\mathbf{P} =-\omega\dfrac{F_o/m}{{\omega_0}^2 -{\omega}^2} F_0 \sin{\omega t}\cos{\omega t}$$. But my book says the mean ...
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0answers
49 views

Constructing a dispersion relation from the Hamiltonian

I'll begin by saying that I'm not entirely clear on if this is possible. I have a Hamiltonian of the form $$ \left( \begin{array}{cccc} \text{$\omega $1} & \text{J12} & 0 & \text{J14} \\ ...
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27 views

Periodically connected QHO's

I've recently been thinking about what happens when you connect quantum harmonic oscillators in a periodic way. I'm actually thinking about when you take a mass-spring system (which can easily be put ...
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30 views

Occurance and disappearance of degeneneracies in a periodic structure of (quantum) LC circuits

Introductory part I'm currently studying an analytical model of coupled LC circuits, in preparation for actually performing measurements on such structures. While the final goal will struggle with a ...
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1answer
57 views

How to find the period of a simple pendulum in an elevator going up with an acceleration?

How to find the period of a simple pendulum in an elevator going up with an acceleration of $a$. Don't just say, $T=2 \pi$ $\sqrt{ \frac l {g+a}}$ I want to know how the above equation is formed.
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2answers
55 views

Is a constant on the RHS of the equation of simple harmonic motion allowed? [closed]

I read at a STEP booklet that we have to know how to bring a simple harmonic motion's equation to the form: $$\frac{\mathrm{d}^2x}{\mathrm{d}t^2} + \omega^2x= c$$ where $c$ is a constant. We also ...
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1answer
16 views

The spring of air: Why does a piston undergo SHM when it is displaced lengthening the air-column inside a cylinder filled with air?

Let there be a cylindrical tube, closed at one-end, with a well-fitting but freely moving piston of mass $m$. [. . .] The piston has certain equilibrium position. If the piston is moved a distance ...
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2answers
64 views

Physical reason behind having greater amplitude when driving frequency$ < $ natural frequency than that when driving frequency $>$ natural frequency

This is quoted from A.P.French's Vibrations & Waves: If the driving force is of low frequency relative to the natural frequency, we would expect the particle to move essentially with the ...
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1answer
43 views

Period of a spring in SHM (simple harmonic motion)

An object with unknown mass M is hanged on a vertical spring with unknown spring constant K, the spring is in rest and is 14 cm from its normal point (if it didn't had the mass hanged it had less 14 ...
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1answer
71 views

Density of states of 3D harmonic oscillator

for the first red box, shouldn't be $\epsilon^2 =\epsilon_{n_x}^2 +\epsilon_{n_y}^2 + \epsilon_{n_z}^2 + 2\epsilon_{n_x}\epsilon_{n_y} + 2 \epsilon_{n_x}\epsilon_{n_z} + ...
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3answers
143 views

Is it possible to write the fermionic quantum harmonic oscillator using $P$ and $X$?

The Hamiltonian of the quantum harmonic oscillator is $$\mathcal{H}=\frac{P^2}{2m}+\frac{1}{2}m\omega^2X^2$$ and we can define creation and annihilation operators ...
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1answer
79 views

Pendulum on the moon, (Highschool)

A simple pendulum used as a clock, set with the correct time at earth, was sent to moon, it was noticed that it is late 36mins for each hour on earth. Calculate the ratio between acceleration of ...
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1answer
58 views

Lax representation of the harmonic oscillator

Peter Lax showed that the differential operators $$L=-6\partial_x^2-u,\quad B=-4\partial_x^3-u\partial_x-(1/2)u_x$$ fulfilling the Lax equation $$\dot{L}+[L,B]=0$$ is equivalent to the KdV equation ...
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0answers
23 views

Cause of SHM of liquid-column in V-tube

Suppose there is a v-shaped tube filled with water. The left limb is at $\theta_1$ & the right limb is at $\theta_2$ with the horizontal base. Initially, the level of water in both the columns are ...
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1answer
43 views

Trick for reformulating in terms of centre of mass and relative variables

I am working through a problem that has caused me difficulties in the past. I have the Hamiltonian $$\mathcal{H}=\frac{p_1^2}{2m_1}+\frac{p_2^2}{2m_2}+\frac{k}{2}(q_1-q_2)^2$$ I want to express the ...
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46 views

Finding the phase space density of $N$ harmonic oscillators

Consider a system of $N$ identical harmonic oscillators in 1d. The Hamiltonian will be given by $$\mathcal{H}_N=\sum_{i=1}^N \frac{p_i^2}{2m}+\frac{m\omega^2}{2}q_i^2$$ Now supposedly the Hamiltonian ...
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0answers
13 views

Where is there posted dampening coefficients for viscous dampers?

Depending on the size of the viscous dampener the coefficient will change, however i am trying to model a "physical" system with calculating everything out, so that way i can test failure before it ...
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1answer
46 views

What are the units of the creation and annihilation operators?

The creation and annihilation operators - also known as ladder operators are; $ \hat{a}^\dagger$ and $\hat{a}$ respectively. Using the equation $\hat{H} = \hbarω\left(\hat{a}^\dagger \hat{a} + ...
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1answer
33 views

Pendulum at an angle

A pendulum has a period of $T$ when swinging from a string. The pendulum is now placed on a frictionless incline at a 30 degree angle. What is the new period of the pendulum?
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1answer
40 views

How to find the spring coefficient of a simply supported beam?

So I've been searching wikipedia and google but nothing can show how to find the spring coefficient of a simply supported beam with a uniformly distributed load. The spring coefficient, $k$, is ...
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0answers
15 views

Usage of concept of static deflection on classical mechanics (ex. SHM based problems)

Can anyone explain how the concept of static deflection (static displacement) is used in problems of SHM? Explanation by/with an illustration would be even the more helpful. Thank you
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2answers
48 views

Using fluid mechanics to show that force is directly proportional to velocity

So I am writing a paper about viscous dampers in harmonic oscilators, however I was looking at some old fluid mechanic notes and I thought I had come across what I needed although I have gotten stuck. ...
4
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2answers
98 views

“Equidistant” spectra in quantum mechanics [duplicate]

In one-dimensional quantum mechanics, it seems that the only kind of potential able to produce an "equidistant" spectrum, i.e. with $E_{n+1}-E_{n}=\text{constant}$, is the harmonic oscillator. Why is ...
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2answers
41 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 ...
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1answer
44 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 ...
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1answer
88 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 = ...
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1answer
56 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 ...
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2answers
537 views

Is the usually taught solution to forced harmonic motion just a special solution?

Let's say we have a mass on a spring being driven by a forcing function. Given hook's law, $F = -kx$, and a forcing function of $$F(t) = F_0\sin(\omega t) .$$ We can write: $$ m\frac{d^2x}{dt^2} = ...
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1answer
56 views

Reflection of Sound wave (Pressure Wave)

I want to study about the phenomenon of reflection of pressure waves as in an open ended organ pipe. Please suggest a suitable resource? I know about the harmonics in a stretched string and I can use ...
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0answers
61 views

discrepancy in theoretical and natural frequency?

In an experiment to determine the natural frequency of a spring-mass-pulley system, why would the experimental natural frequency (found using 1/time) be greater than the theoretical natural frequency ...
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1answer
23 views

Can the logarithmic decrement be found from extension of spring?

Consider a spring-mass system in which a mass hangs freely from a spring fixed to a ceiling. Can the logarithmic decrement be found simply from the extension of the spring? The only parameters known ...
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1answer
48 views

Problem about a spring which oscillates due to a external force [closed]

A person holds a spring of stiffness $k= 80$ N/m by its extremity A; In the other end there is a mass of $0.5$ kg. The spring is initially at equilibrium, when the person starts to shake the ...
2
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1answer
79 views

Meaning of “vacuum state”?

I just learned about $|0\rangle$ and siblings $|0_\gamma\rangle$ and $|0_\infty\rangle$ while studying coherent and squeezed states in a QM class, and I have a question about the meaning of ...