Chapter 2

Question 1

What does it mean when we say that a separable solution of the Schrodinger equation is a stationary state?

Answer 1

Every expectation value is constant in time

Question 2

What does it mean when we say that a separable solution of the Schrodinger equation is a state of definite total energy?

Answer 2

A separable solution has the property that every measurement of the total energy is certain to return to the value E

Question 3

What are some properties of the functions Ψ_n(x) in an infinite square well?

Answer 3

They are alternately even and odd, each successive state has one more node as you go up in energy, they are mutually orthogonal, they are orthonormal, they are complete (any other function can be expressed in a linear combination of them)

Question 4

Do operators commute (ie is xp̂ = p̂x)?

Answer 4

No

Question 5

What is the difference between phase velocity and group velocity?

Answer 5

Phase velocity is the speed of individual ripples in a wave packet and group velocity is the speed of the wave packet

Question 6

What solutions to the Schrodinger equation are normalizable and which aren’t?

Answer 6

Infinite square wells and harmonic oscillators are normalizable, free particles are not