Spherical Harmonics

Question 5: Spherical harmonics (20 points)... | Filo

Consider the three spherical harmonics (a) Ye, o, (b) Y2-y, and (c) Y3 3 (a) For each spherical harmonic, substitute the explicit form of the function taken from Table 7 F. 1 into the left-hand side of eqn 7F.8 (the Schrödinger equation for a particle on a sphere) and confirm that the function is a solution of the equation; give the corresponding eigenvalue (the energy) and show that it agrees with eqn 7 F.10. (b) Likewise, show that each spherical harmonic is an eigenfunction of lz=(ħ/ i)(d / d