Consider a particle with charge e moving under a three dimensional isotropic harmonic potential: in an electric field a) write the unperturbed and perturbed hamiltonian. b) find the exact energy eigenvalues of the particle in the perturbed state. find the degeneracy for the first and second excited state.

Tafari worked one summer on a ship that set weather buoys in the ocean. he watched how one of the buoys moved in the water. describe which parts of the wave would cause the buoy to bob up and down. which wave property determined how fast the buoys bobbed in the water? he observed that when the wind blew harder, the ocean waves were larger, and the buoys moved away from the ship. what effect, if any, did the waves have on how far the buoys moved? explain your answer.

Let v1, v2, w be three linearly independent vectors in r 3 . that is, they do not all lie on the same plane. for each of the following (infinite) set of vectors, carefully sketch it in r 3 , and determine whether or not it is a vector space (i.e., a subspace of r 3 ). explain your reasoning

What type of nuclear decay causes the atomic number of an element to increase by 1?