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

CHAPTER: 10, 11, 12, AND 13.

Please solve the following problems.

57. Two particles with mass m are in harmonic potential V[x] = % kxz. Find the three lowest energy eigenstates and eigenvalues and net spin angular momentum for this system of two particles when the particles have (a) Spin 1 and are non-identical. (b) Spin 1 and are identical bosons. (c) Spin % and are non-identical. (d) Spin % and are identical fermions 58. For a hydrogen atom whose state at: = 0 is given by '1' = A 11/300 + L 1,0211 + \\If (11100 3 E (a) Determine the expectation value of the energy (b) Determine the expectation value of L2 (c) Determine the expectation value of LI 0 0 L to which a 00 x x perturbation of the form 6 V 2 V0 1% is added. (a) Calculate to lst order in the perturbation, the correction to the energy of the nth state. (b) Calculate to lst order in the perturbation, the correction in the wavefunction of the nth state. (c) Calculate to 2nd order in the perturbation, the correction to the energy of the nth state