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

CHAPTER: 7, 8 AND 9.

Please solve the following problems.

39. Show that in quantum mechanics 2 = (rxp) =p - (r . p) (r . p) +in(r . p). Use the Levi-Civita symbol, AXB = Eejk A; BK x; and the commutators between components of r and p. j k 40. Use the ladder operators to determine the matrix elements of Lx, i.e. (l', m' | Lx | I, m). Show the form of the matrix up to ? = 2. 41. Consider a system which is described by the state 14 ) = [1, 0) - i [1, -1) - 00 1 - DO I W V 16 12, -1) + A |1, 1) where A is a constant. (a) Assuming A to be real, calculate A in order for ly) to be normalized. (b) Find L- ly) (c) Calculate the expectation values of Ly and 12 for the state ly). (d) Find the probability associated with a measurement that gives 1 h for the z-component of the angular momentum. (e) Calculate (@ | Lz | y) and