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Detailed
Syllabus and Text References
Topic |
Chapter
G |
| Quantum
interference; De Broglie relation; Particle-wave duality;Wave
function; The Schroedinger equation; Operator of momentum;
The probability current; Statistical nature of predictions
of Quantum Mechanics, Measurements in Quantum Mechanics.
|
1.4,
2.1, 2.2, 2.3,2.4, 2.6, 2.7 |
| Quantum
Mechanics of one-dimensional systems; Stationary states;
Boundary conditions; Infinite potential well; Bound states
and scattering states, discrete and continuous spectrum;
Parity; Dirac notations; Transmission and reflection amplitudes. |
3.1,
3.3, 3.4, 3.6, 4.1,4.2, 4.3, 4.5, 4.6, 4.7, 6.2 |
| The
general mathematical structure of Quantum Mechanics; Linearity
and principle of superposition; Operators; Eigenfunctions
and eigenvalues; Hilbert space; Pure and mixed states;
Commuting operators; Expectations values and measurements;
Heisenberg uncertainty relations. |
5.1,
5.2, 5.3, 5.4 |
| 2D
rotationally invariant systems; Separation of variables
in Schroedinger equation; Operator of angular momentum;
2D harmonic oscillator: rotational basis and Cartesian
basis; Rotational spectrum of a 2D diatomic molecule;
3D rotationally invariant systems; Operator of angular
momentum: commutations relations and eigenstates; Rotational
spectrum of a 3D diatomic molecule; Hydrogen atom. |
7.1,
7.2, 7.3, 8.1, 8.2, 8.3 |
Time
independent non-degenerate perturbation theory;
Time independent degenerate perturbation theory *;
Time dependent perturbation theory;
Transition rates and the Fermi golden rule.
|
11.1,
11.2, 11.3,14.4,15.1, 15.2, 15.3 |
Spin
and Pauli matrices;
Spin in magnetic field. |
10.1,
10.2, 10.4, 10.5 |
Systems
of identical particles, fermions and bosons;
Pauli exclusion principle for fermions
|
13.1,
13.2, 13.3, 13.4,14.1, 14.2, 14.3, 14.5 |
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