Chapter 2: Steps Towards Wave Mechanics

Question 1

You should be able to provide a motivation for the time-dependent Schrödinger equation as discussed in lectures, i.e., by finding a wave equation satisfying E = hbarω and E = p ² /2m starting from the classical wave equation

Answer 1

Question 2

You should know the time-dependent Schrödinger equation (TDSE)

Answer 2

Question 3

Answer 3

Question 4

You should also know the TISE and be able to write it down

Answer 4

Question 5

You should know, and be able to show, that the time dependence for a closed system is given by

Answer 5

Question 6

You should know that if ψ(x) is a solution to the TISE, then the time dependent solution to the TDSE is

Answer 6

Question 7

Be able to solve the TISE in a region of constant potential, V(x) = V0, for E > V0 and show that the solutions are

Answer 7