Effect of the raising operator on an l=1 m=1 state

[neish88]

Pretty basic question but I was wondering what the result of acting the raising operator on an l=1, m=1 quantum state for a hydrogen wavefunction would be.

Specifically,

L₊|1,1> = ?

I know that normally L₊|l,m>=hbar(l(l+1)-m(m+1))^1/2|l,m+1> but I wasn't sure if the eigenstate remained the same (since m cannot be larger than l) or if it results in zero, like if you were to act the lowering operator on the lowest possible state.

Thanks in advance!

 

[malawi_glenn]

it will be zero

L+ on |L,L> = 0

since M_max = L

Same with L- on |L,-L>

since M_min = -L

 

[neish88]

Much appreciated thank you!