Quantum Mechanics

Objectives:

PHYS201 offers a systematic introduction to fundamental non-relativistic quantum mechanics.

Content:

The course introduces Schrödinger equations with solutions in simple potentials, including

harmonic oscillator, spherically symmetric potentials with hydrogen-like atoms. Axioms of quantum mechanics are introduced; matrix representation of quantum mechanics is discussed together with approximate methods (the variational method, perturbation theory, Born approximations). Program also covers spin and angular momentum representations and addition rules and identical particles treatment.

On completion of the course

the student should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The student has gained knowledge about

• basic non-relativistic quantum mechanics
• the time-dependent and time-independent Schrödinger equation for simple potentials like for instance the harmonic oscillator and hydrogenlike atoms, as well as the interaction of an electron with the electromagnetic field
• quantum mechanical axioms and the matrix representation of quantum mechanics
• approximate methods for solving the Schrödinger equation ( the variational method, perturbation theory, Born approximations)
• spin, angular momentum states, angular momentum addition rules, and identical particles

Skills

The student is able to

• apply principles of quantum mechanics to calculate observables on known wave functions
• solve time-dependent and time-independent Schrödinger equation for simple potentials
• apply the variational method, time-independent perturbation theory and time-dependent perturbation theory to solve simple problems
• combine spin and angular momenta

General competence

The student has gained

• general experience with non-relativistic quantum mechanics that is useful for further studies in theoretical physics, as well as nanotechnology
• knowledge about fundamental quantum mechanical processes in nature
• experience using mathematical tools to construct approximate quantum mechanical models