Quantum Mechanics Lecture Notes

Lecture № 1. Physical principles of quantum mechanics. Wave packets. Uncertainty relations.

Lecture № 2. Spreading of wave packets. "Principles" of quantum mechanics. The Schrodinger equation (ScEq). Density of the probability flux vector.

Lecture № 3. Examples of the time-independent Schrödinger equation solution: an infinitely deep one-dimensional rectangular potential well, a three-dimensional potential box.

Lecture № 4. Examples of the time-independent Schrödinger equation solution:linear oscillator; transmission and reflection through a potential barrier (a rectangular step and a rectangular barrier)

Lecture № 5. Mathematical apparatus of quantum mechanics: linear operators.

Lecture № 6. Mathematical apparatus of quantum mechanics: representation theory, physical quantities and operators.

Lecture № 7. Physical quantities and operators (next). Eigenfunctions (EF) and eigenvalues (EV) of the coordinate and momentum operators in the position and momentum representations. The Hamiltonian, stationary states. ScEq in the momentum representation.

Lecture № 8. Solution of the problem of a one-dimensional delta-well in the momentum representation. Commutators and measurement results. Heisenberg inequalities.

Lecture № 9. A complete set of physical quantities. The angular momentum operator.

Lecture № 10. Differentiation of operators with respect to time. Heisenberg representation of operators. Ehrenfest's theorems. Conservation laws.

Lecture № 11. Parity conservation Law. The uncertainty relation for time and energy. Movement in the central field (part).

Lecture № 12. Analysis of the features of motion in the central field (continued). Spherical waves. One-electron atom. Accidental degeneration.

Lecture № 13. Motion in the field of a one-dimensional periodic potential. ShEq in a magnetic field. Motion of an electron in a uniform constant magnetic field. Landau levels .

Лекція № 14. Perturbation theory (PT): Time-independent PT without degeneracy. Time-independent PT with degeneracy. Time-dependent PT.

Lecture № 15. Quasiclassical approximation. The Bohr-Sommerfeld quantization rule. Energy levels of a linear linear oscillator in the semiclassical approximation.

Lecture № 16. Energy levels of a particle in a one-dimensional infinite rectangular potential well in the semiclassical approximation. Tunneling. The quasiclassical transparency coefficient. Theory of the alpha decay.