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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Eigenstates of half Harmonic Oscillator

This might be a stupid question so pardon me! If I am looking for energy eigenstates to the 1D quantum problem such that there is an infinite barrier at $x<0$ and for $x>0$ the potential is ...
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168 views

Why are particles in harmonic motion in normal modes?

Why do we assume that in normal modes, particles oscillate in form cos (wt) ? How do we know that the general motion of particles can be expressed as a superposition of normal modes? In both French ...
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421 views

Equations of motion for bob-on-a-string — am I missing some terms?

The dynamics of a type of physical system I am currently working on are modeled in most of the literature by replacing the moving parts of that system with an equivalent set of pendulums. Parameters ...
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52 views

Is there an equation that tells you more about the amplitude of an object which is in resonance?

I'm a high school senior and I have to write a paper about resonance and differential equations. I've been searching the Internet for a long time, but I haven't found an equation that is properly ...
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1answer
302 views

Is the number-phase uncertainty relation classical?

For a harmonic oscillator in one dimension, there is an uncertainty relation between the number of quanta $n$ and the phase of the oscillation $\phi$. There are all kinds of technical complications ...
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923 views

Probability for harmonic oscillator outside the classical region

I'm having some trouble finding an expression for the probability to find the particle outside the classical area in the harmonic oscillator. I have a wavefunction defined as: $\psi \left( x,\,t ...
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97 views

Is it possible to find a “replacement pendulum” for a system of two equal but perpendicular pendulums?

I ask this question, because at the end of this long day I'm just too dazed to derive the proofs myself (even though I know that I should feel ashamed for this). So, the question: Given two ...
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187 views

The Hamiltonian for clocks?

I am rather a theoretician and looking for a formalism to represent biological clocks by Hermitian operators. The simplest thought model I am looking for is a formal representation of a clock (for ...
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1answer
160 views

Simple pendulum and planet mass [closed]

A simple pendulum, $20cm$ in length, has the period of $2.7s$ on a certain planet. Find the mass of the planet if its diameter is $18000km$. $G=6.67\times10^{-11}Nm^2/kg^2 $ I have no idea how to get ...
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38 views

Delivered/Reflected Power by Drive on a Hamiltonian System

Imagine a SHO with a drive F(t). (or in general a Hamiltonian system) What is the power delivered to the system and can we talk about the power reflected? is i am imagining say a MW oscillator ...
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0answers
110 views

Number theoretical function applied in physics? [closed]

I have a series of number theoretic phenomena (mathematics) that I can describe exactly by the superpositions or linear combination of the below function (I know it is an inverse Fourier type). Does ...
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1answer
115 views

One body harmonic oscillator states expressed in terms of creation operators

I am reading trough chapter one of Moshinsky's "The harmonic Oscillator in Modern Physics". However i am having some trouble with the mathematics in section 8 of chapter 1. I will sketch a summary of ...
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54 views

Doubt about coordinates and point of equilibrium

I'm solving an exercise about small oscillations and I have a doubt about coordinates that I have to use. This is the text of the exercise: "A bar has mass M and lenght l. Its extremity A is hooked ...
2
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1answer
217 views

Harmonic oscillator - wavefunctions

I understand now how I can derive the lowest energy state $W_0 = \tfrac{1}{2}\hbar \omega$ of the quantum harmonic oscillator (HO) using the ladder operators. What is the easiest way to now derive ...
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1answer
39 views

Is there a term for the argument of the sine function outside of geometry?

Are there similar terms in other areas for the idea the "angle" conveys in geometry? I find that functions for abstract things such as pressure, electrical currents (nothing geometric there) on AC ...
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2k views

Origin of Ladder Operator methods

Ladder operators are found in various contexts (such as calculating the spectra of the harmonic oscillator and angular momentum) in almost all introductory Quantum Mechanics textbooks. And every book ...
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138 views

Undamped oscillations. Why is the solution a linear combination of $\sin()$ and $\cos()$?

$ma = mg - cx$, where $x(0) = x_0 = 0$ is the position in which there is no tension in the rope. $dx/dt = v_0$ for $t = 0$; $v_0$ is a known constant. The discriminant of the characteristic ...
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942 views

Effective mass in Spring-with-mass/mass system

Suppose you have a particle of mass $m$ fixed to a spring of mass $m_0$ that, in turn, is fixed to some wall. I'm trying to calculate the effective mass $m'$ that appears in the law of motion of the ...
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3answers
958 views

Hilbert space of harmonic oscillator: Countable vs uncountable?

Hm, this just occurred to me while answering another question: If I write the Hamiltonian for a harmonic oscillator as $$H = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 x^2$$ then wouldn't one set of ...
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3answers
351 views

Complex energy eigenstates of the harmonic oscillator

Given the Hamiltonian for the the harmonic oscillator (HO) as $$ \hat H=\frac{\hat P^2}{2m}+\frac{m}{2}\omega^2\hat x^2\,, $$ the Schroedinger equation can be reduced to: $$ \left[ ...
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1answer
1k views

SHM of floating objects

If we consider an object undergoing who has an acceleration proportional to the displacement of the object, it is going simple harmonic motion. In terms of Newton's second law, this is $$ -\dfrac k ...
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1answer
111 views

2nd order pertubation theory for harmonic oscillator

I'm having some trouble calculating the 2nd order energy shift in a problem. I am given the pertubation: $\hat{H}'=\alpha \hat{p}$, where $\alpha$ is a constant, and $\hat{p}$ is given by: ...
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Time period for spring connected body

Two identical springs with spring constant $k$ are connected to identical masses of mass $M$, as shown in the figures above. The ratio of the period for the springs connected in parallel (Figure 1) ...
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1answer
138 views

Energy eigenvalues of a Q.H.Oscillator with $[\hat{H},\hat{a}] = -\hbar \omega \hat{a}$ and $[\hat{H},\hat{a}^\dagger] = \hbar \omega \hat{a}^\dagger$

I just finished deriving the commutators: \begin{align} [\hat{H}, \hat{a}] &= -\hbar \omega \hat{a}\\ [\hat{H}, \hat{a}^\dagger] &= \hbar \omega \hat{a}^\dagger\\ \end{align} On the ...
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1answer
379 views

Eigenfunctions in a harmonic oscillator

This assignment is about the one dimensional harmonic oscillator (HO). The hamiltonian is just as you know from the HO, same goes for the energies, but I get that the wavefunction of the particle, at ...
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1answer
984 views

Pendulum in an elevator

Suppose we have a pendulum tied to the ceiling of an elevator which is at rest. The pendulum is oscillating with a time period $T$, and it has an angular amplitude, say $\beta$. Now at some time ...
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317 views

Pendulum Wave Period

Recently I've seen various videos showing the pendulum wave effect. All of the videos which I have found have a pattern which repeats every $60\mathrm{s}$. I am trying to work out the relationship ...
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2answers
429 views

Proof for commutator relation $[\hat{H},\hat{a}] = - \hbar \omega \hat{a}$

I know how to derive below equations found on wikipedia and have done it myselt too: \begin{align} \hat{H} &= \hbar \omega \left(\hat{a}^\dagger\hat{a} + \frac{1}{2}\right)\\ \hat{H} &= ...
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126 views

How does one subtract two light beams?

From what I understand, it seems like you can only "add" beams together. You can use a beam combiner, basically using a beam splitter in reverse, to combine two beams. In homodyne detection, you use a ...
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2answers
246 views

Probability of position in linear shm?

The problem that got me thinking goes like this:- Find $dp/dx$ where $p$ is the probability of finding a body at a random instant of time undergoing linear shm according to $x=a\sin(\omega t)$. ...
3
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1answer
525 views

Schrödinger equation for a harmonic oscillator

I have came across this equation for quantum harmonic oscillator $$ W \psi = - \frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2} + \frac{1}{2} m \omega^2 x^2 \psi $$ which is often remodelled by defining a new ...
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1answer
58 views

What is $\gamma$ in the damping equation?

$x''+\gamma x'+w_0^2x=0$ That is the general equation for damped harmonic motion. What is the term or name that describes $\gamma$? Is it called the damping constant? I know its the ration between ...
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Quantum harmonic oscilator - book that does it all right [duplicate]

I am dealing with quantum harmonic oscillator. In every single book or video i have checked out i can read how the mathematical technique for solving this Schrödinger equation: $$ W\psi = - ...
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122 views

Harmonic oscillator with light damping

My textbook gives the following for x as a function of time for a lightly damped harmonic oscillator: $$ x = Ae^{- \gamma t} \cos (\omega \, t)$$ for $\gamma = \dfrac b {2m}$. It says this implies ...
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Why is the damping force on a spring oscillator linearly dependent on velocity?

If you consider the damping force is friction like in: then the force should be $$F=\mu N$$ where $\mu$ is the coefficient of kinetic friction. Why then is the damping force assumed to be linearly ...
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Relativistic genarization of Quantum Harmonic Oscillator

I am trying to find out relativistic description of a quantum harmonic oscillator. For a classical relativistic oscillator mass is a function of co-ordinates(http://arxiv.org/abs/1209.2876). ...
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1answer
453 views

Compound pendulum clarification?

I read in a book the following about compound pendulum and small displacements: There are two points only for which the time period is minimum. there are maximum 4 points for which the time ...
2
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1answer
149 views

A good theoretical approximation for a magnetically damped pendulum

In a laboratory course we had to perform an experiment with a pendulum (just an iron weight on a wire) and play around for some time with its wire's length and so on. This was quite boring and we ...
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1answer
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Standing Waves: finding the number of antinodes [closed]

A string with a fixed frequency vibrator at one end forms a standing wave with 4 antinodes when under tension T1. When the tension is slowly increased, the standing wave disappears until tension T2 is ...
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2k views

Calculating phase difference of sound waves

An observer stands 3 m from speaker A and 5 m from speaker B. Both speakers, oscillating in phase, produce waves with a frequency of 250 Hz. The speed of sound in air is 340 m/s. What is the phase ...
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39 views

How can I find the frequency? [duplicate]

Grocery stores often have spring scales in their produce department to weigh fruits and vegetables. The pan of one particular scale has a mass of 0.5 kg, and when you place a 0.5 kg sack of potatoes ...
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309 views

Doubling the energy of an oscillating mass on a spring [closed]

From this question: Question 1. What do we need to change in order to double the total energy of a mass oscillating at the end of a spring? (a) increase the angular frequency by $\sqrt{2}$. ...
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199 views

Potential energy during vertical fall

Suppose I have a weightless spring connected perpendicularly to the ground, and it has on top of it some weightless surface. Now, I release some sticky object from height $h$ above the system of light ...
2
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1answer
416 views

Simple harmonic oscillator system and changes in its total energy

Suppose I have a body of mass $M$ connected to a spring (which is connected to a vertical wall) with a stiffness coefficient of $k$ on some frictionless surface. The body oscillates from point $C$ to ...
3
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1answer
229 views

The issue on existence of inverse operations of $a$ and $a^{\dagger}$

I have asked a question at math.stackexchange that have a physical meaning. My assumption: Suppose $a$ and $a^\dagger$ is Hermitian adjoint operators and $[a,a^\dagger]=1$. I want to prove that ...
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118 views

Does spatial coupling prohibit resonances due to an external source field?

The harmonic oscillator coupled to a sinodial external source $$\frac{\partial^2 x(t)}{\partial t^2}+\omega_0^2 x(t)=F_0\sin(\omega_\text{ext}\ t),$$ has the solution $$x(t)=x(0)\cos(\omega_0 t)+C ...
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1answer
412 views

Accessible microstates of harmonic oscillator in microcanonical enemble

While reading up on statistical physics, I am going through the calculation of the partition function of the harmonic oscillator in the microcanonical ensemble. The result for the partition function ...
2
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1answer
144 views

Why uncertainity is minimum for coherent states?

While reading for quantum damped harmonic oscillator, I came across coherent states, and I asked my prof about them and he said me it is the state at which $\Delta x\Delta y$ is minimum. I didn't ...
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1answer
149 views

Hyperbolic, parabolic, elliptical PDE related to under-, critical- and overdamped in harmonic osciallation

A damped harmonic oscillator has three cases for the damping: underdamped, critically damped and overdamped. With partial differential equations, I know the hyperbolic wave equation, the parabolic ...
2
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1answer
182 views

Coordinate representation of quantum ladder operator?

I can't seem to figure out how to derive the coordinate representation of the $a_+$ ladder operator in quantum mechanics. I know that $a_-$ is $\sqrt{\frac{1}{2mwh}} (mwx + i\dot{p}) $ in which where ...