Consider the 3-dim Harmonic Oscillator for which the time-independent Schrodinger Equation is + 2x 2 2 y ( x, y, z ) + - k ( x2 + y2 + z2 ) us (x, y, z) = Ey (x, y, z) 2m Using separation of variables, one obtains the following eigenfunctions and Energy eigenvalues: (You might enjoy trying to obtain this result) Vnx,ny,n (x, y, z) = Wn (x) Wn (y) yn, (z) Enxnyan = nextn tn, + N/ W two where n , n , n, = 0, 1, 2, 3, ... and yn, (x), Wn (y) and y, (z) are one-dimensional Harmonic Oscillator eigenfunctions. a. Find the values of the four lowest energy states in terms of hwo. 3 5 7 9 Answer: -hwo , -hwo, 2 2 -hwo , - hwo, 2 2 b. Find the degeneracy of each of these four levels. Answer: 1, 3, 6 and 10