Course name: Quantum Mechanics I

Course status: compulsory

Course language: polish

Name of the teacher: prof. dr hab. Piotr Magierski

Semester: 4

Number of hours: 2/ 2/ _ (Lect/Classes/Lab)

Code:

Number of ECTS credits:

Pre-requsites: Classical Mechanics, Classical Electrodynamics

Form of completion: Exam (written)

Assessment methods: Student has to complete classes before is allowed to take the final exam. To complete classes student has to pass two exams. Homeworks and activity during classes are also graded. Those with outstanding records will pass final exam automatically with the best
grade. Details are presented at the beginning of the course.
Final grade=2/3*(final exam)+1/3*(class)

Aims of the course: During the lecture student gets acquainted with quantum mechanics of one and two-particle systems. He/she learns wave mechanics based on Schroedinger equation, together with elements of more abstract formulation in Hilbert space. The aim of the course is to teach a student how to solve typical quantum mechanical problems such as: tunneling probability through a potential barrier, calculation of eigenenergies using perturbation theory, finding probability of quantum transition in an external time-dependent potential, etc. Moreover the course provides a thorough knowledge of concepts forming foundations of quantum mechanics and is supposed to familiarize a student with surprising and sometimes counter-intuitive consequences of quantum mechanics.

Program:

1. Review of most important experiments contradicting classical physics. Old quantum theory.
2. Schroedinger equation. Probabilistic interpretation of wave function.
3. Operators of physical quantities. Eigenfunctions and eigenvalues.
4. Measurement in quantum mechanics. Expectation value. Ehrenfest theorem. Heisenberg uncertainty principle.
5. Free particle motion. Wave packet. Eigenfunctions of momentum operator. Normalization in a box.
6. Linear harmonic oscillator. Energy levels, wave functions.
7. Motion in a spherically symmetric potential. Angular momentum operator.
8. Hydrogen atom.
9. Abstract formulation of quantum mechanics. Hilbert space. State vector. Dirac 'bra' and 'ket' notation. Unitary transformations. Projection operators. Evolution of quantum system as a unitary transformation.
10.Creation and annihilation operators for harmonic oscillator.
11. Spin. Motion in a magnetic field. Zeeman effect.
12. Perturbation theory in quantum mechanics. Fermi golden rule.
13. Measurement in quantum mechanics revisited: EPR paradox, Bell's inequality, quantum teleportation.

Basic literature:

L. Schiff, Mechanika kwantowa, PWN 1997

A.S. Dawydow, Mechanika kwantowa, PWN 1969 .

L.D. Landau, E.M. Lifszyc, Mechanikakwantowa, PWN 1979

I. Białynicki-Birula, M. Cieplak, Teoria kwantów, PWN 1991

B. Średniawa, Mechanika kwantowa, PWN 1981