Whats perturbation theory?
We are not covering this, but there is one idea related to it you need to understand: if you add a new potential to the Hamiltonian, such as that due to a magnetic field, then strictly you have to solve for the bound state wavefunctions all over again, and in general the wavefunction solutions of the Schrödinger equation won’t be the same as before. However, if the extra “perturbing” potential is small, the wavefunction solutions will be nearly the same, and the effect of the new potential is mostly just to shift the energy eigenvalues a little bit. Later courses treat this sort of problem in more general terms, and it can be shown that the assumption that the wavefunction solutions are the same is a reasonable one.
