Keble A3 and Mathematical Methods - Hilary Term

Schedule:

Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8
Monday     Homework 1 Homework 2 Homework 3 Homework 4 Homework 5  
Tuesday
Wednesday
Thursday Tutorial 1 Tutorial 2 Tutorial 3 Tutorial 4 Tutorial 5
Friday

Tutorials this term will be taught by Dr. Oliver Lunt. Homework is always due at 7pm, on Mondays in weeks 3–7

Tutorials always run 2pm-6pm, on the days indicated. From 2pm-4pm, we will have a session with all students, from 4pm-6pm we will run half-hour paired tutorials.

HT Tutorial 1

Material: Angular momentum and 3D potentials
Reading: Gasiorowicz Ch 7; Shankar Ch 12

Class Question: What defines a set of operators to be angular momentum operators?

Essay: There is no essay this week.

Problem Sheet: problem_sheet_HT1.pdf

HT Tutorial 2

Material: The Hydrogen atom, spin
Reading: Gasiorowicz Ch 8, 10; Shankar Ch 13, 14

Class Question: Is spin different from classical rotation of a particle? If so, how? (Continued from essays)

Essay: Discuss the interpretation of spin as intrinsic angular momentum. Is spin different from classical rotation of a particle? If so, how?

Problem Sheet: problem_sheet_HT2.pdf

HT Tutorial 3

Material: Addition of angular momenta, two particles
Reading: Gasiorowicz Ch 10-5, 10-A; Shankar Ch 15

Class Question: What are triplet and singlet states?

Essay: Discuss Clebsch-Gordan coefficients giving their physical interpretation.

Problem Sheet: problem_sheet_HT3.pdf

HT Tutorial 4

Material: The "real" Hydrogen atom, perturbation theory
Reading: Gasiorowicz Ch 8, 11, 12

Class Question: When does perturbation theory work? Is it ever guaranteed to work?

Essay:Discuss the main physical effects ignored with our earlier treatment of the H-atom and explain qualitatively how they alter the spectrum.

Problem Sheet: problem_sheet_HT4.pdf

MT Tutorial 5

Material: Helium atom and Zeeman effect
Reading: Gasiorowicz Ch 13,14; Shankar 10

Class Question: Which physical effects cause the states of the first excited level in Helium to split?

Essay Question: Essay: Explain how atomic states and emission lines are split in the presence of a static B field.

Problem Sheet: problem_sheet_HT5.pdf

HT Vacation assignment

Please submit before Wednesday (Week 0). We will discuss this during the first session in TT.

Material: Exchange symmetry
Reading: Gasiorowicz Ch 13; Shankar 10

Essay: Look up and discuss the spin-statistics theorem. Relate what you find to the statistical physics of identical particles?

Problem Sheet: problem_sheet_HT_vacation.pdf