PHY-301 Quantum Mechanics I
Pre-requisites: PHY-101, PHY- 104, PHY- 203
PART A
1. Physical Basis
- Failures of classical mechanics and emergence of quantum mechanics
- Bohr atom and old quantum theory
- Domain of quantum mechanics
- Heisenberg uncertainty principle
2. Formulation
- Concepts and postulates of Quantum Mechanics
- Operators and commutation of operators
- State function and state function space
- Hilbert space
- Eigenvalue equations
- Eigenfunctions and basis vectors
- Hermitian operators
- Orthogonality and the sharing of eigenfunction sets
3. Schrodinger's Equation
- Hamiltonian operator
- Time dependent and time independent Schrodinger's equations
- Time variation of expectation values
- Probability current density
- Ehrenfest's theorems
PART B
4. Problems in One-Dimension
- Potential Step
- Potential barrier
- Potential well
- Quantum mechanical tunneling
5. Harmonic Oscillator
- Solution of Schrodinger's equation for the one dimensional harmonic oscillator
- Eigenvalues and eigenfunctions of harmonic oscillator
- Expectation values of some observables for the pure and mixed states of harmonic oscillator
6. Hydrogen Atom
- Schrödinger’s equation for the hydrogen atom in spherical coordinates
- Angular momentum; Operators in Cartesian coordinates
- Commutation relations
- Angular momentum operators in spherical polar coordinates
- Solution of the angular and radial part of the Schrödinger’s equation of the hydrogen atom
Recommended Books
Griffiths, David J. Introduction to Quantum Mechanics.
Quantum Mechanics – Nouredine Zettili – 3rd, 2022 – John Wiley & Sons
| Syllabus | Zettili sections to read | Priority | |
|---|---|---|---|
| 1. Physical Basis | Ch. 1: 1.1.1, 1.1.2, 1.2, 1.3, 1.4, 1.5.1, 1.6, 1.7 | ⭐⭐⭐ | |
| 2. Formulation | Ch. 2: 2.2, 2.3, 2.4.1–2.4.6, 2.4.9, 2.5, 2.6, 2.7; Ch. 3: 3.2–3.5 | ⭐⭐⭐⭐⭐ | |
| 3. Schrödinger Equation | Ch. 3: 3.6.1–3.6.5, especially 3.6.3–3.6.5; 3.8.2 | ⭐⭐⭐⭐⭐ | |
| 4. Problems in One Dimension | Ch. 4: 4.4, 4.5, 4.5.1–4.5.3, 4.6, 4.7 | ⭐⭐⭐⭐⭐ | |
| 5. Harmonic Oscillator | Ch. 4: 4.8, 4.8.1–4.8.5 | ⭐⭐⭐⭐⭐ | |
| 6. Hydrogen Atom | Ch. 5: 5.2–5.5, 5.7; Ch. 6: 6.3.1, 6.3.2, 6.3.5; Appendix B: B.2–B.3 | ⭐⭐⭐⭐⭐ | |
