THERE ARE ONLY 2 QUESTIONS RELATED TO QUANTUM PHYSICS: PHY256: IF YOU CAN ONLY HELP WITH A HANDWRITING AND NOT TYPED, I WOULD REALLY APPRICIATE IT. THANK YOU VERY MUCH IN ADVANCE:

Q#3: Consider a hydrogen atom at I = 0 in the superposition state: (,0 = A (Magma - 1,030+ 3 W32: - 4 2/1334). [A is a normalization constant, and lit/"h,\" are orthonormal eigenstates with quantum numbers n, I. m,.] (a) Calculate the expectation values , and . [Give answers in units of either it or eV] (b) A measurement at t > 0 finds the angular momentum of the atom to be J5 h in magnitude. At this time, what is the probability of finding the atom to have no angular momentum about the ZaXis? At a later time, is there any probability of finding the atom to have finite angular about the Xaxis or yaXis? Q#4: Consider an electron beam of energy E=4V0 skimming a potential step U(x) as shown below: (a) Determine the unnormalized wave function in each region (I, II, III), and specify boundary conditions. (b) Derive an exact expression for the transmission probability T in terms of V0, L, h and me