Sho Definition and 57 Threads

  1. E

    Bullet Impact Speed Calculation: 2.25x10^3 N/m

    A 0.0125 kg bullet strikes a 0.300 kg block attached to a fixed horizontal spring whose spring constant is 2.25 * 10^3 N/m and sets it into vibration with an amplitude of 12.4 cm. What was the speed of the bullet if the two objects move together after impact? E = .5 k A2 = .5 m v2 Do I use m =...
  2. D

    SHO with a fixed boundary

    How to solve the time-independent Schodinger equation with the following potential: U(x)=x^2 for x>x0 U(x)=infinity for x<x0 ?
  3. quasar987

    Calculating Probability of Simple Harmonic Oscillator in Phase Space

    Consider a simple harmonic oscillation in 1 dimension: x(t)=Acos(wt+k). If the energy of this oscillator is btw E and E+\delta E, show that the probability the the position of the oscillator is btw x and x+dx is given by P(x)dx=\frac{1}{\pi}\frac{dx}{\sqrt{A^2-x^2}} Hint: calculate the volume...
  4. S

    What are the energy levels and wavefunctions of a 3D SHO potential well?

    We have a particle moving in a 3-D potential well V=1/2*m*(omega^2)*(r^2). we use separation of variables in cartesian coords to show that the energy levels are: E(Nx,Ny,Nz)=hbar*omega(3/2 + Nx + Ny + Nz) where Nx,Ny,Nz are integers greater than or equal to 1. Therefore we can say that...
  5. R

    .Solving [X,H] for the SHO Hamiltonian

    [x, H]= ?? Given the Hamilton operator for the simple harmonic oscilator H, how do I get to [X, H]= ih(P/ m)? I put X in momentum representation, but then I can't get rid of these diff operators. mmh? thanks in advance
  6. M

    Average potential and kinetic energy of SHO

    I am using Frenches book on waves and have a question. You have a standard driven damped oscillator and I am suppose to find the average potential and kinetic energy of it. They are both similar so I will just use the potential for example. I took \frac{1}{T}\int^T_0 \frac{1}{2}KX^2 dt Where...
  7. Z

    Why is the Commutator Between Ladder Operators for a SHO Not Zero?

    Hi, Having trouble understanding something here, hoping someone can help...when dealing with a SHO, we can define two ladder operators a and a-dagger. The way I understand it is, applying a-dagger to an eigenstate of H (and that has, for instance, eigenvalue E) will give us a new eigenstate...
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