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

CHAPTER: 5, 6 AND 9.

34. A particle is described by the following wave function within an infinite potential well with infinite potential 0 x 2a/3 (a) What is the probability that the particle occupies the nth state of the infinite potential well? (b) What is the expectation value of the energy for this state? 35. Determine the expectation value of px for the first excited state of the harmonic oscillator using the explicit wavefunction as a function of x. 36. (a) Express px in terms of the operators a and a of the harmonic oscillator. (b) Calculate (p x)nm (c) Compare your answer with that calculated for the first excited state in Prob. 35. 37. Using the raising and lowering operators, determine the expectation value of p x in the nth harmonic oscillator state, i.e. (n |p2 x2 \ ). 38. (a) Find the ground state wavefunction for the potential V[x] = _ kx2 x 2 0 and V[x] = co x 0. This problem requires thought not mathematics