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# Quantum Mechanics 2

Vak
2018-2019

Quantum Mechanics 1, Statistical Physics 1, Classical Mechanics B, AN3na, LA2na

## Description

The usefulness of quantum mechanics does not stop with the analytical solution of the Bohr model of the hydrogen atom. This course deepens the understanding of quantum mechanics by studying important quantum phenomena and applications of quantum mechanics in technologies like MRI and the laser.

This comprises the study of indistinguishable quantum particles and their statistical distributions and the use of perturbation methods to understand the energy levels of atoms. The details of the observed emission spectrum of hydrogen are inconsistent with the Bohr model and simple analytical solutions of the Schrödinger equation. Most notably, the so called spin-orbit coupling gives rise to small shifts and splittings of the Bohr levels. The coupling of an atom to an external oscillating field gives rise to stimulated emission and can be understood in the framework of time-dependent perturbation theory.

The following topics are treated:

• Quantum statistical description of indistinguishable particles

• Fermi-Dirac, Bose-Einstein, and Planck distribution

• The free electron gas, Bose-Einstein condensation, and the law of Stefan and Boltzmann.

• The structure of atoms and the Periodic Table

• Time-independent perturbation theory and application in the fine-structure and hyperfinestructure of the hydrogen atom

• Influence of external magnetic field (Zeeman-effect) and electrical field (Stark-effect) on spectral lines

• Time-dependent perturbation theory and application to two-level systems

• Nuclear magnetic resonance and its use in Magnetic Resonance Imaging (MRI).

• Einstein theory of radiation processes: absorption, stimulated and spontaneous emission and its use in the laser.

• selection rules for radiative transitions
An introduction to more advanced and/or modern topics in quantum mechanics is given: entanglement, quantum information, Dirac equation.

## Course objectives

After the course the student you will be able to discuss and explain the following concepts and topics and to apply these concepts in calculations.

• Quantum statistical description of indistinguishable particles

• Fermi-Dirac, Bose-Einstein and Planck distribution

• Properties of the free electron gas, the free Bose gas, and the role of the density of states

• How quantum mechanics averts the ultraviolet catastrophy

• Apply time-independent perturbation theory to calculate the fine-structure and hyperfinestructure of the spectrum of hydrogen atoms

• How external magnetic (Zeeman-effect) and electrical fields (Stark-effect) affect the spectra of atoms

• Apply time-dependent perturbation theory to two-level systems and explain the essence of magnetic resonance imaging

• Explain the radiative processes: absorption, stimulated and spontaneous emission (Einstein theory) and perform calculations of the corresponding transition rates.

You will be able to explain or describe in your own words the following concepts or topics:

• How the laser (and maser) work

• Entanglement and quantum information

• Dirac equation for relativistic electrons

## Algemene Vaardigheden (Soft Skills)

• You are able to paraphrase your reasonings clearly

• You plan your time in such a way that your study load is well divided over the various study activities that are needed in this course: studying the book, preparing and making exercises

Schedule

## Mode of instruction

Lectures, tutorials (exercise classes) and homework assignments

Total course load 5 EC = 140 hours, of which 42 hours are spent attending lectures and tutorials (11x2 hours lectures + 10x2 hours tutorials). Approximately 40 hours are needed to study the course material. The remaining 58 hours are spent on completing the assignments and preparing for the exam

## Assessment method

Written exam (closed book) with open questions.
The final grade is calculated using the grade of the exam and adding a bonus of maximally 1 point to be earned by handing in homework assignments. For the retake exam the bonus does not apply.

## Blackboard

Course material is on blackboard

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