Entry requirements

Linear algebra. Multivariable analysis. Transform Methods. Mechanics I+II. Electromagnetism I, Waves and optics. Mathematical Methods of Physics or equivalent courses.

Learning outcomes

The course treats concepts and working methods that are used within modern physics, in particular the physics of electrons in materials. On completion of the course the student shall be able to:

• describe and explain the correspondence principle and its interpretation.
• use with the language of basic quantum mechanics and formalism and describe quantum phenomenon within the electron physics of materials with this formalism.
• carry out elementary theoretical studies and calculations of atoms and molecules from quantum mechanical relations.
• carry out spectroscopic studies of different subjects and interpret the results in quantized units.
• report on future applications of quantum physics within technical development and society.

Content

The basic phenomena of the quantum physics and experimental background, the wave-particle duality, particles and atomic models. Black-body radiation, line spectra, Rutherford's atomic model . The photon, photoelectric effect, Compton-dispersion. Bohr's atomic model, the Balmer series.

The wave function and the Schr?dinger equation. Wave packets, probability interpretation, Heisenberg's uncertainty relations. Stationary states. Expectation values, the continuity equation and Ehrenfest's relations. Operators.

One-dimensional systems, Transmission and reflection. Eigenvalue problem.

Three-dimensional systems. Orbital angular momentum and central motion. Spin. Addition of angular momentum. Identical particles.

Simple perturbation theory.

One-electron atoms: The Schr?dinger equation, energy eigenvalues wave functions, transitions, energy level diagram. The Born-Oppenheimer approximation. Optical spectroscopy on the hydrogen atom.

Many-electron atoms: The central field approximation, orbital angular momenta, spin, the Pauli exclusion principle, antisymmetric wave functions, quantum number sets. Zeeman effect, electron configurations, periodic system, spin-orbit coupling, terms, fine structure levels, Hund's rules. Generation of optical transitions and X-ray radiation and its spectroscopies.

Diatomic molecules:

Binding, molecule potentials, the molecular orbital model, electron configurations. Energy level diagrams (Grotrian diagram), molecular orbitals, molecular terms. Vibration and rotational motions, transitions.

Fermions and Bosons. Electron binding and energy bands in solid materials. Bose-Einstein condensation.

Interpretations of quantum mechanics, Bell's inequality, quantum cryptography and quantum computers.

Laboratory work: Photoelectric effect. Optical spectroscopy (H + N2). X-ray spectra (fluorescence, element analysis).

Instruction

Lectures, lesson exercises, experimental and computer-based laboratory sessions. Compulsory seminars and supervisions in small groups. Teaching may sometimes be given in English.

Assessment

Written examination at the end of the course (9 of 10 credits). To pass the course, a passed laboratory course is also required (1 of 10 credits). Laboratory reports and assignments or half-time examinations form together with the written examination the basis for the final grade. If a bonus system is used, the bonus is only valid at the final examination and at first regular re-examination.