I am now solving a Schrodinger equation with a magnetic field: $$i\hbar U_{t}-V(x)U-0.5\left(\frac{\hbar}{i}-B(x)\right)^2U=0$$ where $V$ is a real and smooth potential and $B$ is the magnetic field which has to satisfy Gauss' law: $$\nabla \cdot B=0.$$
By now, I have tried $$B=\text{constant}$$ and $$B=\cos(\vec{k} \cdot \vec{x}-kct),$$ but the result is weird when comparing to the graph of the original equation ($B=0$).
I don't know what the solution is supposed to look like when adding different $B$ and I am wondering if I should use some other magnetic field.