BOOK: Quantum Mechanics, A Paradigms Approach, David H. McIntyre

CHAPTER: 7, 8 AND 9.

Please solve the following problems.

48. (a) Using the results for hydrogen-like atoms, calculate the energy of the ground state glln=1lf=01m=0 and the first excited states 911,1: 1'?! m for the following systems: (1) doubly ionized lithium (2) positronium (an electron and positron orbiting each other) and a (3) a muon orbiting a proton (b) For each of the above systems, calculate the wavelength of radiation corresponding to a transition between the rst excited state and the ground state. (c) For each of the above systems, calculate (r) for each state. Note: calculate (r) for a general Z, n and reduced mass and then substitute the appropriate values for the above systems. (d) For each of the above systems, determine the root-meansquare velocity. Note: determine vrms for a general system from the Virial theorem and then substitute the appropriate values. 49. (a) Calculate the probability that an electron in the ground state girn=1,;=0,m=o can be found within the radius of the proton rproton = 1.2 x 10']5 m. (b) Repeat calculation for a muon orbiting the proton. 50. For an electron in a hydrogen atom in the 3 d state. (a) Determine the most probable distance between the electron and proton, i.e. at what distance does r2 IR32|2 have a maximum. (b) Compare this distance with (r) (c) What is the width of the probabiity density distribution Ar = ((r (r))2) in this state