4. consider a particle constrained to move on the surface of a sphere of radius a. take the center of the sphere as the origin of coordinates. the potential is then of the form r a (a) give the hamiltonian operator for the particle in spherical coordinates, and write out the t-independent schroedinger equation. (b) to make life easy ignore the angular dependence of the potential, i. e., set u(0, o) uo, where uo is a constant. what are the energy levels?

Ascientist is working with a new kind of quantum dot to make a dye. he is applying newton’s laws to the particle, but it seems to be breaking these laws of physics. which action will most likely the scientist study the particle’s motion? a. he needs to remember that the particle is too large for quantum analysis. b. he must continue to use newtonian mechanics, but he needs to learn more about the particle. c. he needs to use quantum mechanics, not newtonian mechanics, because this is a nanotechnology product. d. he must determine new physical laws that only apply to quantum dots.