QM Lecture 8

Ref: This lecture follows closely The Feynman Lectures, Vol III, Chapter 8 and Chapter 9

The Hamiltonian Operator: How do quantum states change with time (10-20-2022)
8.1 What are the base states?
8.2 How do states change with time?
8.2.A The Time Evolution Operator
8.2.B The Hamiltonian Matrix
8.3 General characteristic of the Hamiltonian Matrix
8.3.A Symmetry of the H matrix
8.3.B Stationary states
8.3.C Interpretation of the Hamiltonian Matrix as the Energy Matrix
8.4 Two-State Systems Figuring out the Hamiltonian Matrix
8.4.A The ammonia molecule
8.4.A.a Case: Absence of crosstalk
8.4.A.b Case: Quantum Tunneling
Figuring out the Hamiltonian Matrix
Time evolution of the quantum states
Conservation of the total probability
Stationary states
8.4.B Ammonia molecule under a static electric field (10-25-2022)
8.4.C Molecule in a time dependent electric field
Operation of the ammonia maser
Particular case: Transitions at resonance
General case: Transitions off resonance, w≠wo.
8.4.D Quantum mechanics calculation of the Einstein’s coefficients
Stimulated emission and stimulated absorption coefficients
Spontaneous emission coefficient
Classical analogy of spontaneous emission

Appendix: Light-Matter Interaction: Einstein's Law of Radiation

8.5 Other Examples of Two-state System
8.5.A The hydrogen molecular ion

Appendix: Transformation of Coordinates Under the Rotation of Coordinates