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.

learn more… | top users | synonyms (1)

4
votes
2answers
102 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 ...
-3
votes
0answers
24 views

SHM by using cos equation [on hold]

A particle start motion according to equation $x=a\cos \left(\omega t+ \frac{\pi}{6}\right)$. Find time required for it to reach mid point. The displacement according to it must be 0 but how?
0
votes
0answers
22 views

Finding the amplitude of a pendulum [closed]

I'm tring to simulate the behaviour of a pendulum. I have it in the equilibrium position, then I apply on it an initial velocity $\vec{v_{0}}$ Knowing $\vec{v_{0}}$ and its mass m, how can I find the ...
0
votes
1answer
108 views

Understanding an equation in quantum mechanics (J. J. Sakurai, “Modern QM”, eq. 2.3.13) [closed]

Hello, It is from quantum mechanics book of sakurai. You can see equation 2.3.12b implies 2.3.13. But my question is, how? Could you please show me how can i bring equation 2.3.13 from 2.3.12b ...
4
votes
2answers
81 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 ...
1
vote
0answers
74 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 = ...
1
vote
1answer
57 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 ...
1
vote
0answers
28 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 ...
1
vote
1answer
25 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 ...
0
votes
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 ...
0
votes
1answer
42 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 = ...
0
votes
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 ...
0
votes
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 ...
0
votes
0answers
41 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} \\ ...
0
votes
0answers
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 ...
0
votes
0answers
29 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 ...
-5
votes
1answer
51 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.
0
votes
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 ...
0
votes
1answer
14 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 ...
2
votes
2answers
58 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 ...
0
votes
1answer
29 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 ...
0
votes
1answer
59 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} + ...
3
votes
3answers
126 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 ...
0
votes
1answer
74 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 ...
1
vote
1answer
51 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 ...
1
vote
0answers
22 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 ...
0
votes
1answer
40 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 ...
0
votes
0answers
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 ...
1
vote
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 ...
1
vote
1answer
45 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} + ...
1
vote
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?
1
vote
1answer
38 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 ...
0
votes
0answers
12 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
1
vote
2answers
44 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
votes
2answers
91 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 ...
1
vote
2answers
38 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 ...
-3
votes
1answer
42 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 ...
5
votes
1answer
85 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 = ...
0
votes
1answer
52 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 ...
6
votes
2answers
528 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} = ...
0
votes
1answer
44 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 ...
0
votes
0answers
59 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 ...
0
votes
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 ...
1
vote
1answer
45 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
votes
1answer
78 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 ...
0
votes
0answers
50 views

Effect on Q factor and resonant frequency when scaling down a damped oscillator to micro / nano scales

I've always just accepted that as you scale down a mechanical system the frequency and Q factor both increase. But how exactly do they scale? Linearly? With the square of reduction in size? Or maybe ...
-1
votes
2answers
70 views

Acceleration of Simple pendulum [closed]

A simple pendulum starts its motion from one extreme when it left at extreme it starts its motion towards the extreme and its velocity become increase and become maximum at mean position and also ...
0
votes
1answer
34 views

Quantum harmonic ocillator and the mean energy U(T)

The energy of a quantum harmonic oscillator is given by: $$E(n)=\hbar\omega\left(n+\frac{1}{2}\right)$$ The canonical partition function is given by: $$Z(T)=\sum_{n=o}^\infty e^{-\beta ...
0
votes
2answers
44 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 ...
0
votes
1answer
33 views

Mass-Spring system on an accelerating jet

Imagine a perfect mass spring system. If it's put on an accelerating plane, how will the motion change? Is the plane's acceleration like a driving/damping force, where: $$F_{\text{driving}} = ...