Consider the harmonic oscillator - Consider the harmonic oscillator, for which the general solution is
x(t) = A cos(wt) + B sin(wt)
1. Express the energy in terms of A and B and show it is time independent.
2. Choose A and B suc ...
Ehrenfest's equations and harmonic oscillator - Using Ehrenfest's equations show that for the harmonic oscillator the average values of p and x display classical behavior for any initial state.
Harmonic Oscillator - Consider the 1-D harmonic oscillator, with Hamiltonian H=p²/2m+½mw²x²=hw(a†a+1/2), and with energy eigenstates H|n}=En|n}=hw(n+1/2)|n}. The eigenvectors of the annihilation operator a are known ...