Problem Set 05 - Physics 424 Quantum Mechanics Fall 2015 Reading\/Homework Assignment 5 Due in Class Friday Note The first mid-term exam will be based on

# Problem Set 05 - Physics 424 Quantum Mechanics Fall 2015...

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Physics 424: Quantum Mechanics, Fall 2015 Reading/Homework Assignment 5 Due in Class Friday, 10/16/15 1 Note The first mid-term 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 Spin-1/2 Particle in a Magnetic Field. This section is not needed for the problems below and will not be on the first mid-term, 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. (3.128-3.129)) 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