Schedule:
| Week 1 | Week 2 | Week 3 | Week 4 | Week 5 | Week 6 | Week 7 | Week 8 | |
| Monday | Homework 2 | Homework 3 | Tutorial 3, Homework 4 | Homework 5 | Homework 6 | |||
| Tuesday | Homework 1 | |||||||
| Wednesday | ||||||||
| Thursday | Tutorial 1 | Tutorial 2 | Tutorial 4 | Tutorial 5 | Tutorial 6 | |||
| Friday |
Homework is always due at 7pm, on Mondays in weeks 3–7 (Tuesday week 1)
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.Material: Linear Algebra; Vector spaces; Introduction to QM and Dirac notation
Reading: Gasiorowicz Ch 1; Shankar Ch 2, 3
Class Question: Why can the double slit experiment with electrons not be described by classical wave theory? Essay: Discuss the way probabilities enter into quantum mechanics. How does this differ from classical physics?
Problem Sheet: problem_sheet_MT1.pdf
Material: Linear Algebra; Hermitian matrices and diagonalization; The Schrödinger equation
Reading: Gasiorowicz Ch 2, 3.1, 3.2; Shankar Ch 4.3
Class Question: What are stationary states and how are they related to diagonalization? Essay: How does the Schrödinger equation differ from the classical wave and diffusion equations? What are the consequences?
Problem Sheet: problem_sheet_MT2.pdf
Material: Hermiticity, orthogonality, Sturm-Liouville problem; Particle in a box
Reading: Gasiorowicz Ch 3.3 to 3.6; Shankar Ch 5.2, 9
Class Question: Is the discrete “quantized” spectrum found in some quantum systems surprising? Can it occur in classical systems? What is different when we see this in quantum mechanics? Essay: What are the postulates of Quantum mechanics? How can we motivate the measurement postulate, by thinking about an example of two entangled spins or otherwise?
Problem Sheet: problem_sheet_MT3.pdf
Material: PDEs, Operators
Reading: Gasiorowicz Ch 3.2, 3.3, 3.6, 9; Shankar Ch 1, 5.2
Class Question: Why are Hermitian and unitary operators important in quantum mechanics?
Note: No essay this week (to allow more time to familiarise yourself with Mathematica)
Mathematica Notebook: QuantumMechanicsAndMM.nb Problem Sheet: problem_sheet_MT4.pdf
Material: Fourier series and transforms; Operators and measurements
Reading: Gasiorowicz Ch 5, 6.1; Shankar Ch 4, 9
Class Questions: How do measurements change the state of a system if the outcome is not revealed? Is there a connection between the Heisenberg uncertainty principle and the Fourier transformation? Essay Question: Discuss the energy-time uncertainty relation [see, e.g., p. 250 in Quantum Mechanics I, C. Cohen-Tannoudji, B. Diu, and F. Laloe (John Wiley & Sons)]
Problem Sheet: problem_sheet_MT5_new.pdf Mathematica Notebook: PotentialWell_questions.nb
Material: The quantum harmonic oscillator
Reading: Gasiorowicz Ch 4.7, 6.4; Shankar Ch 7
**Class Question: ** Why is the quantum harmonic oscillator important? Essay: Describe the connection between classical motion in a quantum harmonic oscillator and coherent states.
Problem Sheet: problem_sheet_MT6_new.pdf
Please submit before Wednesday (Week 0). We will discuss this during the first session in HT.
Material: One-dimensional problems, entanglement
Reading: Gasiorowicz Ch 4.7, 6.4; Shankar Ch 7
Essay: Write 1 page describing the phenomenology of entanglement. What does the existence of entanglement signify that is special in quantum mechanics with respect to Classical Mechanics? And how is this illustrated with the discussion of Schrödinger’s cat?
Problem Sheet: problem_sheet_MT_vacation.pdf