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 ...
Mean position in a 1-D harmonic oscillator - Obtain the mean position, , for a particle moving in a 1-D harmonic oscillator potential, when the particle is in the state with normalized wavefunction:
Y(x)= ((a/(4*pi))^.25)*(2ax^2-1)*exp((-a ...
Bohr radii and energy levels. - An electron of mass m is in a circular orbit in the potential U=0.5 k r^2. Using Bohr's quantization rule, find the allowed orbital radii and energy levels of this electron.