4. Eigenvalue problem for L₂. The z component of orbital angular momentum is given in position representation by hə ide

[answerhappygod]

1 (30 KiB) Viewed 33 times

4. Eigenvalue problem for L₂. The z component of orbital angular momentum is given in position representation by hə ide (ny) (L₂): so the eigenvalue problem for L, is of form ħ ə i do (1) where q is the eigenvalue. For simplicity, let the eigenfunction be (p) = (ny) and let the eigenvalue be q = mħ. Find (p) by solving the differential equation (1) and apply the boundary condition (p) = (p +27) to obtain the allowed values of m. The physical significance of the boundary condition is that and +27 represent the same physical position and so the value of must be same whether we take or + 2π or plus any integer multiple of 2. -(n|y) = q(n|u)