# FYSA2032 Quantum Mechanics, part B (4 cr)

Study level:
Intermediate studies
Grading scale:
0-5
Language:
Finnish
Responsible organisation:
Department of Physics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023

## Description

• Schrödinger equation and Hamiltonian in three dimensions.

• Central-force problem, separation of the Schrödinger equation to the angular and radial parts.

• Solution of the angular part of the central-force problem, spherical harmonics.

• Solutions of the radial part for simple piecewise constant potentials (free particle, potential well, finite square well) and the hydrogen atom.

• Eigenstates of angular momentum, orbital angular momentum and spin. General angular momentum and its matrix representation.

• Coupling of angular momenta, singlet and triplet states, Clebsch-Gordan coefficients.

• Two-particle systems, identical particles, bosons and fermions.

• Time independent first- and second-order perturbation theory: The non-degenerate and degenerate cases.

## Learning outcomes

After completing the course the student

• Is able to apply the tools of wave mechanics and formal quantum mechanics, acquired in part A, to the treatment of the three-dimensional Schrödinger equation.

• Can explain the meaning of a central force field and its simple nature, and how it enables the separation of the radial and angular parts of the Schrödinger equation.

• Is able to handle the spherical harmonics, the angular wave function of the central-force problem.

• Can explain qualitatively the nature of the radial wave functions involved in central-force problems.

• Can explain the properties of the eigenfunctions of angular momentum and can form the matrix representation of an angular-momentum operator.

• Is able to couple two angular momenta (spin with spin, spin with orbital, two general angular momenta). Is able to relate the results of angular-momentum coupling to Clebsch-Gordan coefficients.

• Knows how to treat two-particle systems and can construct the wave functions of two identical particles (bosons or fermions).

• Is able to apply time-independent first- and second-order perturbation theory in the non-degenerate and degenerate cases.

## Description of prerequisites

• FYSA2031 Quantum mechanics, part A
• MATP211-213 Calculus 1-3 (in particular derivatives and integrals of basic functions, integration by parts, chain rule of derivatives)
• MATP121, MATA122 linear algebra 1 & 2 (in particular linear vector space, matrices and determinants, the eigenvalue problem and diagonalization)
• MATA114 differential equations (in particular separable and second-order linear differential equations with constant coefficients)
• MATA200 complex calculus (in particular complex conjugation, absolute value)

Luentomoniste

## Literature

• Griffiths: Introduction to Quantum Mechanics. 2nd Edition, Cambridge University Press, ISBN-10 1107179866, ISBN-13 9781107179868.
• Spiegel, Lipschutz, Liu: Mathematical Handbook of Formulas and Tables.

## Completion methods

### Method 1

Evaluation criteria:
Exercises and exam (for example 20 points from the exercises and 40 points from the exam).
Time of teaching:
Period 2
Select all marked parts

### Method 2

Description:
This completion method is intended for students for whom method 1 is not possible for specific reasons (e.g. language, living elsewhere). The course lecturer must be contacted before enrolling on the course.
Evaluation criteria:
Exercises and exam.
Select all marked parts
Parts of the completion methods
x

### Teaching (4 cr)

Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
Exercises and exam (for example 20 points from the exercises and 40 points from the exam).
Language:
Finnish
Study methods:

Exercises and exam.

x

### Independent study (4 cr)

Type:
Independent study
Grading scale:
0-5
Evaluation criteria:
Exercises and exam.
Language:
Finnish
Study methods:

Self-study, exercises, exam.