[spidermclovin]

I've been given the question: "show that the wavefunction ψ = (1/sqrt2pi)e^imlΦ is a solution of the Schodinger equation (-ħ²/2mr²)(d²ψ/dΦ²) = Eψ and hence derive the equation for allowed energies. I'm fine with deriving the energy equation but I don't know how to prove it is a solution 

[Borek]

Have you tried to simply plug the wave function into the equation?

[Enthalpy]

Check that it's a function. That is, it must have the same value after an integer number of turns.

And that it's a solution: d²(e^iΦ)/dΦ² shouldn't be too hard. With all constants.

And that it's normalized: |ψ|² integrates to 1 over the domain, here 0≤Φ<2π.

The more interesting question would have been: why can we write Schrödinger's equation that way? In Δψ, this writing neglects d²ψ over the radial and polar directions despite the variations are steep, and keeps only the dependence on the azimuth rΦ. The reasons aren't bad, but such lacks of explanations make QM abstract.