Well, a classical Hamiltonian is [itex]H=E_{total}=\frac{P^2}{2m}+V[/itex]
In QM this turns to [itex]\hat{H}=\frac{\hat{P}^2}{2m}+V[/itex], where [itex]\hat{P}=-i\hbar\frac{\partial}{\partial x}[/itex] and [itex]\hat{H}=i\hbar\frac{\partial}{\partial t}[/itex].
So Schrödinger's equation is [itex]\hat{H}\psi=\frac{\hat{P}^2}{2m}\psi+V\psi[/itex]
For an electrically charged particle it is: [itex]\hat{P}=-i\hbar(\frac{\partial}{\partial x_{\mu}}-qA_{\mu})[/itex], and remember to add the [itex]\phi q[/itex] to the V term.
For spin, you would have to move on to relativistic QM...
This is covered in Griffiths - Introduction to Elementary Particles, Zee - Quantum Field Theory in a Nutshell, and the classic Peskin, An Introduction to Quantum Field Theory.
be warned, before you tackle these books you need to know what a Lagrangian and Hamiltonian are, what variational math is (e.g. what is a functional), what are canonical variables, etc. (this is covered by analytical classical mechanics - best covered IMO in Goldstein, Classical Mechanics).
And you should know what a four vector is and how to handle tensors.
By the way, there is a *very* slow paced introductory course by Leonard Susskind on youtube.
He's very thorough. start here:
If that's too much for you, try his lectures on classical mechanics and special relativity first.