Quantum question - angular momentum

[bon]

Homework Statement

Please see attached problem

Homework Equations

The Attempt at a Solution

ok so I am trying to solve these three question.. when i understand the method i think i can solve them all.. so please could you help me solve the first 5.3

I understand that L_z = -i d/dphi

but I am not sure how to apply this to the wavefunction to find eigenvalues..

any help would be great!
thanks

 

[bon]

anyone?