The raising and lowering operators change the value of m by one unit: [4.120]where  is som...

The raising and lowering operators change the value of m by one unit:

 [4.120]

where  is some constant. Question: What is  if the eigenfunctions are to be normalized? Hint: First show that  is the hermitian conjugate of L± (since Lx and Ly are observables, you may assume they are hermitian ... but prove it if you like); then use Equation 4.112. Answer:

 [4.121]

Note what happens at the top and bottom of the ladder (i.e., when you apply L+ to  or L- to ).