Suppose a half integer l value, say 1 2, were allowed for orbital angular momentum From we may deduce, as usual, Now try to construct Y 1 2 , 1 2 (,) by (a) applying L to Y 1 2 , 1 2 (,) and (b) usingL to Y 1 2 , 1 2 (,) 0 Show that the two procedures lead to contradictory results (This gives an ar...

Lets work through the two procedures to construct Y12 12 and show that they lead to contradictory re ...

Suppose a half-integer l-value, say 1/2, were allowed for orbital angular momentum. From we may deduce, as

Question:

Suppose a half-integer l-value, say 1/2, were allowed for orbital angular momentum. From

we may deduce, as usual,

Now try to construct Y_1/2,_-1/2(θ,ϕ) by (a) applying L_ to Y_1/2,_-1/2(θ,ϕ); and (b) using L_ to Y_1/2,_-1/2(θ,ϕ) = 0. Show that the two procedures lead to contradictory results . (This gives an argument against half-integer !-values for orbital angular momentum.)