Quantum mechanics basic question on azimuthal wave function.

[Aerozeppelin]

Homework Statement

Applly conditions to azimuthal wave function for an electron in the hydrogen atom to show that ml, the magnetic quantum number, can take on any integer value.

See attachment for actual question.

Homework Equations

I'm pretty stuck, is it something to do with the radial equation? Or separating variables?

The Attempt at a Solution

 

[DrClaude]

An acceptable wave function can only have a single value for any given angle $\phi$.

 

[Aerozeppelin]

Yes, because it is continuous with respect to the variable, and its derivate.

So, would you suggest differentiating the wave function and letting the derivative equal the original wavefunction?


I tried this and got:

m_l = \frac{1}{i}

But I don't see how this shows that m_l can only take the integer values?