In: Physics
Solve the quantum simple harmonic oscillator in three dimensions i.e. find the energy and eigenkets. It's solution will include hermite polynomials.
here
,
and
are principal quantum numbers in x , y and z direction which take
value independent from each other starting from 1 to set pf
positive integers. The final eigen ket in 3-d spaceis the product
of independent eigen ket of a 1-d harmonic oscillator in three
orthogonal directions(x,y and z).