Read about harmonic oscillator | 55 Discussions | Page 1

  1. anaisabel

    Density of states of one three-dimensional classical harmonic oscillator

    ia
  2. S

    Calculating degeneracy of the energy levels of a 2D harmonic oscillator

    Too dim for this kind of combinatorics. Could anyone refer me to/ explain a general way of approaching these without having to think :D. Thanks.
  3. Lo Scrondo

    I Time averages for a 2-dimensional harmonic oscillator

    I'm studying Ergodic Theory and I think I "got" the concept, but I need an example to verify it... Let's take the simplest possible 2D classical harmonic oscillator whose kinetic energy is $$T=\frac{\dot x^2}{2}+\frac{\dot y^2}{2}$$ and potential energy is $$U=\frac{ x^2}{2}+\frac{y^2}{2}$$...
  4. D

    Phase space of a harmonic oscillator and a pendulum

    Hello everybody, new here. Sorry in advance if I didn't follow a specific guideline to ask this. Anyways, I've got as a homework assignment two cannonical transformations (q,p)-->(Q,P). I have to obtain the hamiltonian of a harmonic oscillator, and then the new coordinates and the hamiltonian...
  5. Vivek98phyboy

    I Why is this SHM the way it is?

    I know four different forms in which an SHM can be represented after solving the differential and taking the superposition acos(wt+Ø) asin(wt+Ø) acos(wt-Ø) asin(wt-Ø) where a- amplitude In the above image they took B as negative in order to arrive at acos(wt+e). If i already knew i wanted...
  6. C

    A Please help me understand this HO energy in He4 gas

  7. H

    A Overlap of nth QHO excited state and momentum-shifted QHO ground state

    ##\newcommand{\ket}[1]{|#1\rangle}## ##\newcommand{\bra}[1]{\langle#1|}## I have a momentum-shifting operator ##e^{i\Delta p x/\hbar}## acting on the ground state ##\ket{0}## of the QHO, and I want to compute the overlap of this state with the n##^{th}## excited QHO state ##\ket{n}##. Given...
  8. M

    A rather weird form of a coherent state

    As far as I know we can express the position and momentum operators in terms of ladder operators in the following way $${\begin{aligned}{ {x}}&={\sqrt {{\frac {\hbar }{2}}{\frac {1}{m\omega }}}}(a^{\dagger }+a)\\{{p}}&=i{\sqrt {{\frac {\hbar }{2}}m\omega }}(a^{\dagger }-a)~.\end{aligned}}.$$...
  9. Baibhab Bose

    Effects of KE & PE of a Harmonic Oscillator under Re-scaling of coordinates

    The wavefunction is Ψ(x,t) ----> Ψ(λx,t) What are the effects on <T> (av Kinetic energy) and V (potential energy) in terms of λ? From ## \frac {h^2}{2m} \frac {\partial^2\psi(x,t)}{\partial x^2} + V(x,t)\psi(x,t)=E\psi(x,t) ## if we replace x by ## \lambda x ## then it becomes ## \frac...
  10. PhillipLammsoose

    I Problem with the harmonic oscillator equation for small oscillations

    Hey, I solved a problem about a double pendulum and got 2 euler-lagrange equations: 1) x''+y''+g/r*x=0 2) x''+y'' +g/r*y=0 (where x is actually a tetha and y=phi) the '' stand for the 2nd derivation after t, so you can see the basic harmonic oscillator equation with a term x'' or y'' that...
  11. TheBigDig

    Green's Function for a harmonic oscillator

    I know that due to causality g(t-t')=0 for t<t' and I also know that for t>t', we should get g(t-t')=\frac{sin(\omega_0(t-t'))}{\omega_0} But I can't seem to get that to work out. Using the Cauchy integral formula above, I take one pole at -w_0 and get \frac{ie^{i\omega_0(t-t')}}{2\omega_0} and...
  12. D

    A position of stable equilibrium, and the period of small oscillations

    I tried by taking the derivative of the potential to find the critic points and the I took the second derivative to find which of those points are minimum points. I found that the point is ##x=- a##. I don't understand how to calculate the period, since I haven't seen anything about the harmonic...
  13. G

    Finding the parameters for Harmonic Oscillator solutions

    Homework Statement Using the Schrödinger equation find the parameter \alpha of the Harmonic Oscillator solution \Psi(x)=A x e^{-\alpha x^2} Homework Equations -\frac{\hbar^2}{2m}\,\frac{\partial^2 \Psi(x)}{\partial x^2} + \frac{m \omega^2 x^2}{2}\Psi(x)=E\Psi(x) E=\hbar\omega(n+\frac{1}{2})...
  14. Baynie

    MATLAB Code: Stationary Schrodinger EQ, E Spec, Eigenvalues

    Hello everyone, For weeks I have been struggling with this quantum mechanics homework involving writing a code to determine the energy spectrum and eigenvalues for the stationary Schrodinger equation for the harmonic oscillator. I can't find any resources anywhere. If anyone could help me get...
  15. Rabindranath

    Angular momentum operator for 2-D harmonic oscillator

    1. The problem statement I want to write the angular momentum operator ##L## for a 2-dimensional harmonic oscillator, in terms of its ladder operators, ##a_x##, ##a_y##, ##a_x^\dagger## & ##a_y^\dagger##, and then prove that this commutes with its Hamiltonian. The Attempt at a Solution I get...
  16. LarryC

    Quantum Spherical Pendulum

    I have trouble with finding the eigenstates of a spherical pendulum (length $l$, mass $m$) under the small angle approximation. My intuition is that the final result should be some sort of combinations of a harmonic oscillator in $\theta$ and a free particle in $\phi$, but it's not obvious to...
  17. Sushmita

    A particle of mass 'm' is initially in a ground state of 1- D Harmonic oscillator potential V(x)...

    Homework Statement [/B] A particle of mass 'm' is initially in a ground state of 1- D Harmonic oscillator potential V(x) = (1/2) kx2 . If the spring constant of the oscillator is suddenly doubled, then the probability of finding the particle in ground state of new potential will be? (A)...
  18. K

    I Phase angle of a damped driven harmonic oscillation

    Hello, in every book and on every website (e.g. here http://farside.ph.utexas.edu/teaching/315/Waves/node13.html) i found for driven harmonic osciallation the same solution for phase angle:θ=atan(ωb/(k−mω^2)) where ω is driven freq., m is mass, k is spring constant. I agree with it =it follows...
  19. Safder Aree

    Harmonic Oscillator violating Heisenberg's Uncertainity

    Homework Statement Does the n = 2 state of a quantum harmonic oscillator violate the Heisenberg Uncertainty Principle? Homework Equations $$\sigma_x\sigma_p = \frac{\hbar}{2}$$ The Attempt at a Solution [/B] I worked out the solution for the second state of the harmonic oscillator...
  20. S

    I Entropy Contradiction for a Single Harmonic Oscillator

    Making use of the partition function, it is straight forward to show that the entropy of a single quantum harmonic oscillator is: $$\sigma_{1} = \frac{\hbar\omega/\tau}{\exp(\hbar\omega/\tau) - 1} - \log[1 - \exp(-\hbar\omega/\tau)]$$ However, if we look at the partition function for a single...
  21. WeiShan Ng

    I Distribution of Position in classical & quantum case

    I am confused about the difference between the two In Griffith's 2.3 The Harmonic Oscillator, he superimposes the quantum distribution and classical distribution and says What I understand for quantum case is that ##|\Psi_{100} (x)|^2## gives the probability we will measure the particle...
  22. D

    Mde decomposition of quantum field in a box

    Homework Statement I am considering the Klein Gordon Equation in a box with Dirichlet conditions (i.e., ##\hat{\phi}(x,t)|_{boundary} = 0 ##). 1-D functions that obey the Dirichlet condition on interval ##[0,L]## are of the form below (using the discrete Fourier sine transform) $$f(x) =...
  23. G

    Relativistic Harmonic Oscillator Lagrangian and Four Force

    Homework Statement Consider an inertial laboratory frame S with coordinates (##\lambda##; ##x##). The Lagrangian for the relativistic harmonic oscillator in that frame is given by ##L =-mc\sqrt{\dot x^{\mu} \dot x_{\mu}} -\frac {1}{2} k(\Delta x)^2 \frac{\dot x^{0}}{c}## where ##x^0...
  24. M

    QM: Writing time evolution as sum over energy eigenstates

    Suppose I have a 1-D harmonic oscilator with angular velocity ##\omega## and eigenstates ##|j>## and let the state at ##t=0## be given by ##|\Psi(0)>##. We write ##\Psi(t) = \hat{U}(t)\Psi(0)##. Write ##\hat{U}(t)## as sum over energy eigenstates. I've previously shown that ##\hat{H} = \sum_j...
  25. Y

    Solve a system of two linked harmonic oscillators

    $$m_1 \ddot{x} - m_1 g + \frac{k(d-l)}{d}x=0$$ $$m_2 \ddot{y} - m_2 \omega^2 y + \frac{k(d-l)}{d}y=0$$ It is two masses connected by a spring. ##d=\sqrt{x^2 + y^2}## and ##l## is the length of the relaxed spring (a constant). What is the strategy to solve such a system? I tried substituting...
  26. K

    Calculate the time out of sample points with set frequency

    Hi all, at the moment I am doing my Master Thesis and have the following problem. I am trying to measure Data and asign it a proper timestamp. My problem is, that the data is coming in bursts and the timestamps I assign with the software are wrong. The controller I am using for monitoring the...
  27. WeiShan Ng

    I Why drop the vibrational ground state energy

    This is from *Statistical Physics An Introductory Course* by *Daniel J.Amit* The text is calculating the energy of internal motions of a diatomic molecule. The internal energies of a diatomic molecule, i.e. the vibrational energy and the rotational energy is given by...
  28. D

    I How is the CSCO in an harmonic oscillator?

    Hi everyone, I have a great doubt in this problem: Let a mass m with spin 1/2, subject to the following central potencial V(r): V(r)=1/2mω2r2 Find the constants of motion and the CSCO to solve the Hamiltonian? This is my doubt, I can't find the CSCO in this potencial. Is a problem in general...
  29. V

    Linear perturbation to harmonic oscillator

    Homework Statement Find the first-order corrections to energy and the wavefunction, for a 1D harmonic oscillator which is linearly perturbed by ##H'=ax##. Homework Equations First-order correction to the energy is given by, ##E^{(1)}=\langle n|H'|n\rangle##, while first-order correction to the...
  30. V

    Anharmonic oscillator first-order correction to energy

    Homework Statement I have ##H'=ax^3+bx^4##, and wish to find the general perturbed wave-functions. Homework Equations First-order correction to the wave-function is given by, $$\psi_n^{(1)}=\Sigma_{m\neq n}\frac{\langle\psi_m^{(0)}|H'|\psi_n^{(0)}\rangle}{n-m}|\psi_m^{(0)}\rangle.$$ The...
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