For the case in exercise 1, specialize to an infinitesimal gauge transformation that rotates \(\vec{A}\) in its plane (transverse to \(\vec{B}\) ), and interpret this in terms of the classical motion.

Data From Exercise 1:-

Consider a stationary gauge transformation \(\Lambda(x, y)\) in the plane transverse to a magnetic field \(B_{z}\). Calculate the effect it has on the Schrödinger equation and its solutions.