chemical Engineering

help with a. and b.

The "particle in a one-dimensional bor" problem is one of the simplest problems in quantum mechanics. It refers to an electron confined within a one-dimensional bor with infinile barriers. The eigenstales (or allowed wave functions) of the electron are given by (see Problem 3.5): on(2) = 2 w sin () 7272 W (1.29) where n is an integer (n n defines an eigenstate, 1,2,3,...) and W is the width of the bor. Each value of The corresponding energy eigenvalues are given by 172 E. 272* W2' (1.30) and they are all distinct or non-degenerate, in keeping with what was proved in Problem 1.2. For an election injected into a quantum bor of width W at time t = 0) in the state 3712 0(0) = [iv]sin (**) 972 sin () 7712 W + 2 sin W pilkitkyu) () :)] W (1.31) where the plane of the quantum well is the (r, y) plane: (u) find the value of A. (6) find the wave function at time l. (c) What is the eructation value of the electron's energy