1. A particle of mass m is moving in a one-dimensional potential well given by V(x)=?k2x2/2. The particle is initially in the ground state and is then given a small perturbation in energy, ?E. Find the probability of the particle transitioning to the first excited state.

2. A charged particle of mass m and charge q is moving in a uniform magnetic field B. The particle is initially moving perpendicular to the magnetic field, and has a kinetic energy of K. Find the radius of the particle's circular trajectory.