Physics 424: Quantum Mechanics, Fall 2015
Reading/Homework Assignment 5
Due in Class Friday, 10/16/15
1
Note
The first midterm exam will be based on the readings and problems in the
assignments up to and including this one.
Reading
•
Finish reading Townsend Chapter 3 – Angular Momentum.
•
Townsend Sec. 4.1 – The Hamiltonian and the Schr¨odinger Equation.
•
Townsend Sec. 4.2 – Time Dependence of Expectation Values.
•
Townsend Sec. 4.3 – Precession of a Spin1/2 Particle in a Magnetic
Field. This section is not needed for the problems below and will not
be on the first midterm, but we will start covering it this week.
Problems to work out and turn in (60 pts total)
1. (5 pts) Townsend problem 3.6 – Normalization constant for a lowered
spin state.
2. (5 pts) The generalized uncertainty principle for any two observables
A, B
(Text Eqs. (3.1283.129)) can be written (as we did in class)
Δ
A
Δ
B
≥
1
2
h
ψ

[
ˆ
A,
ˆ
B
]

ψ
i
where

ψ
i
is the state of the system.
However, the expression inside
the the absolute value signs above is
not
the expectation value for a
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 Fall '15
 mechanics, Work, Hilbert space, expectation value, Hermitian