Fizyka Kwantowa - Quantum Physics

The student gets acquainted with quantum mechanics for the system of one and two interacting particles. He learns wave mechanics based on the Schroedinger equation together with elements of more abstract formulation in Hilbert space. The aim of the lecture is to teach the student how to solve specific quantum-related problems mechanical such as: calculating own energy for simple potential wells, own values of observables, etc. In addition, during the lecture the student will learn the concepts forming the foundations of quantum theory, and unexpected and sometimes counter-intuitive predictions of quantum mechanics.

1. Overview of the most important experiments that undermine classical physics. Old quantum theory.
2. Schroedinger equation. Probabilistic interpretation of the wave function.
3. Operators of physical quantities. Own functions and eigenvalues.
4. Measurement in quantum mechanics. Expected value. Ehrenfest theorem. Heisenberg uncertainty principle.
5. Linear harmonic oscillator. Steady-state energies and wave functions.
6. Movement in spherically symmetrical potential. Angular moment operator.
7. Hydrogen atom.
8. Abstract formulation of quantum mechanics. Hilbert space. State vector. Dirac 'bra' and 'ket' notation.
9. Cast operators. Evolution of the quantum system as a unitary transformation. Tensor product of Hilbert spaces - entangled states.
10. Creation and annihilation operators for a harmonic oscillator.
11. Spin angular momentum. Movement of a particle in a magnetic field. Zeeman phenomenon. Pauli equation.
12. Addition of angular momentum in quantum mechanics.
13. Elements of quantum mechanics of many bodies. Particle indistinguishability. Fermions and bosons. Pauli's principle.
14. Variational estimation of the ionization energy of the helium atom.

Notes for a lecture:

HERE (1)

HERE (2)