Hello. I have one question: I want to solve shrodinger equation for a photon. here's what i did:
$$
E\Psi = - \frac{\hbar^2}{2m} \nabla^2 \Psi + V\Psi
$$
$$
-\frac{2Em}{\hbar^2} \Psi=\nabla^2\Psi - \frac{2mV}{\hbar^2} \Psi
$$
$$
\nabla^2\Psi - \frac{2mV}{\hbar^2}\Psi +\frac{2Em}{\hbar^2} \Psi =0
$$
$$
\nabla^2 \Psi -\frac{2m}{\hbar^2}\left(V-E\right) \Psi = 0
$$
$$
\nabla^2\Psi +\frac{2m}{\hbar^2}(E-V)\Psi=0
$$
$$
E = \hbar f
$$
$$
\nabla^2\Psi+\frac{2m}{\hbar^2}(\hbar f-V)\Psi =0
$$
$$
V =0