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: 

Prerequsites: 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


Aims of the course: During the lecture student gets acquainted with quantum mechanics of one and twoparticle 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 timedependent 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 counterintuitive 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. BiałynickiBirula, M. Cieplak, Teoria kwantów, PWN 1991 B. Średniawa, Mechanika kwantowa, PWN 1981 