Sho Definition and 56 Threads

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 ?

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...

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...

[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

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...

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...