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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How To Use Ladder Operators?

I'm studying for a test in quantum mechanics and I'm having a hard time understanding how to use ladder operators. There are no examples in my text book, only definitions that I can't understand how ...
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326 views

Determining the spring constant in an oscillation problem [closed]

A 130g air-track glider is attached to a spring. The glider is pushed in 10.4cm and released. A student with a stopwatch finds that 14.0 oscillations take 19.0s I would like to know why the ...
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Conservation of energy in a quantum harmonic oscillator after a sudden change in spring constant

At a given instant of time, a harmonic oscillator undergoes a sudden change in spring constant from $k$ to $k'$. Show that for energy to be conserved in the accompanying transition, $\sqrt{k/k'}$ must ...
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81 views

Interpretation of Free Damped Vibrations

I'm studying vibrations; so I'm using Beer-Johnston-Cornwell Dynamics book. I am worry about the equation for Underdamped Vibration, which in the book it is: $$x_{(t)}=x_0e^{-\lambda ...
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55 views

LC Oscillator and relativity

There are two identical LC oscillators with electronic counters attached indicating how many times they have oscillated (from the time they are turned on). They are turned on simultaneously and one is ...
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63 views

Infinite period in Simple Harmonic Motion

I'm studying the Simple Harmonic Motion, and I am hesitant about, how to get mass values for infinite period? When mass is 0. When mass is infinite. With $\tau=2\pi/\sqrt{k/m}$.
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214 views

Harmonic Oscillator (Quantum Mechanics)

Griffiths uses an algebraic "brute force" technique to solve the harmonic oscillator. I'm somewhat confused regarding a few parts. $$\frac{1}{2m}[p^2 + (m \omega x)^2] \psi = E \psi$$ $H = ...
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369 views

Two-block system connected to a spring

Say you have two blocks with masses $m_1$ and $m_2$, where $m_1>m_2$. The smaller block sits atop the larger block. The larger block is connected to a spring, which is then connected to a wall a ...
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214 views

Quantum harmonic Oscillator analytic method

I'm using a book from Griffiths, I got really stuck about how he arrived at the approximate solution, is it just by trying( trial solution method?), I really appreciate any help on this. ...
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144 views

Finding the tangential force experienced by a bob of mass m on a simple pendulum via the gradient/nabla operator)

The problem was posed as follows. Given a pendulum of length $L$ with a mass $m$ attached to it, which forms an angle $\theta$ from the y-axis to the direction of swinging. First we had to find the ...
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67 views

Spring with changing equilibrium

Suppose that we have two cars on a track, each with a different mass. Now suppose that the cars are connected with a spring. We smack one car. I would like to write down the equations of motion for ...
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A basic question about Heisenberg State Kets (in particular the simple harmonic oscillator)

I know base kets in the Heisenberg picture are $U^\dagger |{a}\rangle$ but if the base kets are the base of the hamiltonian, and the hamiltonian is independent of time, are all of the base kets ...
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Average Energy of the Quantum Harmonic Oscillator

In Griffiths, the average potential energy for the quantum harmonic oscillator is given as $$<V>=\frac{1}{2}\hbar \omega(n+\frac{1}{2})$$ Is the potential energy of the quantum harmonic ...
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591 views

Expectation value of total energy for the quantum harmonic oscillator [closed]

A particles unnormalized wavefunction is given as $$\psi(x)=2\psi_1+\psi_2+2\psi_3.$$ How can I find $\langle E\rangle $ without calculating $\langle T\rangle$ or $\langle V\rangle $ ...
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660 views

Simple harmonic oscillator: zero point energy?

Today we had a lecture on the simple harmonic oscillator and its quantum mechanical treatment. My teacher derived the equation for it and finally concluded it has some zero point energy. My ...
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142 views

“Complex Variables Method” in Diff. Eq. - Justification and physical meaning?

A common method of simplifying calculations that involve differential equations - particularly involving oscillation - is to replace $\cos(\theta)$ with $e^{i \omega t}$, evaluate, and then take the ...
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367 views

Vibration of pulley and string system

So here's the statement: A pulley of a mass $M$ is hanged using a spring (stiffness of the string being $k_1$), as shown in the image. What is the frequency of the pulley's oscillation? So that's ...
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172 views

Measure energy state of quantum harmonic oscillator

When discussing the quantum mechanical harmonic oscillator we are talking about energy eigenstates. How would one actually measure in which state an harmonic oscillator is in? Could you weigh it and ...
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757 views

Equations of motion for a spherical pendulum in a non-inertial reference frame

Take a spherical pendulum with bob mass $m$, rod length $\ell$ and physical coordinates $\theta$, $\phi$ (spherical angles) and $h$ (the hinge height with respect to the coordinate origin). The rod is ...
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992 views

Equations of motion for a pendulum and spring system

The question is available here: I've modeled the building as a rod on a torsional spring (with a pendulum hanging from the top). $\phi$ is the angle from the centre for the pendulum and $\theta$ ...
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236 views

Coupled Oscillators

This is an exercise of my last exam. Since I couldn't find anybody who solved it or knows how to, it would be really nice if somebody could tell me if my thoughts on it go into the right direction. ...
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680 views

Hermite polynomials for expected value of harmonic oscillator

This was a problem on my final exam that has been really bugging me. Consider the quantum Harmonic oscillator prepared in an energy eigenstate, $\psi_n$(x). Calculate the expectation value of the ...
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182 views

Can soldiers marching at the right frequency realistically cause a bridge to break?

In my physics class it was suggested that ancient armies had a rough understanding of the idea of a resonant frequency and so they "broke step" when crossing bridges so as to avoid a very high $Q$. I ...
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Second Quantization - Texts

I am trying to familiarize myself with the ideas of Second Quantization. However, the literature that I can find online seems only to outline the tools of this formalism of quantum mechanics. There ...
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153 views

Quantum Mechanics Basics: product space

Consider a coupled harmonic oscillator with their position given by $x_1$ and $x_2$. Say the normal coordinates $x_{\pm}={1\over\sqrt{2}} (x_1\pm x_2)$, in which the harmonic oscillators decouple, ...
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835 views

Why doesn't mass of bob affect time period?

Please correct me if I'm going wrong - By the gravitation formula: $F = \frac{G m_1 m_2}{r^2} $, So if the mass of a bob is greater then the torque on it should increase because the Force increased ...
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646 views

Energy transfer in a coupled pendulum

If you take a look at this video you will see what kind of a coupled pendulum I'm talking about. So I made a similar one in my high school's physics lab, using light metal bobs(much lighter than the ...
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39 views

Organs & Oscillations: An Analysis on the Temperature Dynamics of Solids

Does temperature have an influence on the frequency of an oscillating organ pipe?
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57 views

Mass frequency problem

For Dispersion relation , according to Gaussian profile, the author in the equation 3 wrote as $\omega= \left(k^2+\omega_{mass}^2\right)^{1/2}$ My question is what is mass frequency and how it arose ...
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Periodic sequence with exponentially increasing period?

I have to develop a physical model for a certain type of biological oscillation that can be built upon periodic sequences. From earlier questions I know that any periodic sequence (containing $0$s ...
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229 views

Oscillation with exponentially increasing period

I am trying to build a model for a certain type of oscillatory behaviour with a kind of exponential dilatation. How can I modify the function of a simple cosine oscillation $\psi(x)=A_0 \cos(2\pi\; ...
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666 views

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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1answer
159 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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292 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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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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240 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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692 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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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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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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131 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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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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109 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
106 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 ...
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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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38 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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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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130 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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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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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 ...