PROVIDE FULL SOLUTION
PROVIDE FULL SOLUTION
PROVIDE FULL SOLUTION
Consider the 3-dimensional Harmonic Oscillator for which the time-independent Schrödinger Equation is
PROVIDE FULL SOLUTION
PROVIDE FULL SOLUTION
1
Consider the 3-dimensional Harmonic Oscillator for which the time-independent Schrödinger Equation is
h^2
a^2
y(x,y,z) - (kx+y+z)y(x,y,z) = Ey(x,y,z)
2m
o^2
Using separation of variables, one obtains the following eigenfunctions and Energy eigenvalues: (You might enjoy trying to obtain this result) W_n(x)W_n(y)W_n(z)
E_n = (n_x + n_y + n_z + 1)h
where
n_x, n_y, n_z = 0, 1, 2, 3, ...
and x, y, and z are one-dimensional Harmonic Oscillator eigenfunctions.
a. Find the values of the four lowest energy states in terms of h
Answer: -h^2/2m, h^2/2m, 3h^2/2m, 5h^2/2m
b. Find the degeneracy of each of these four levels
Answer: 1, 3, 6, and 10