(Created 2010-07-25.)

QUANTUM MECHANICS AND MATHEMATICAL METHODS | FMFF15 |

**Aim**

The student should after completing the course have a basic knowledge of quantum mechanics and mathematical methods of physics in order to continue studies in specializations towards nanophysics, highspeed- and nanoelectronics and photonics.

*Knowledge and understanding*

For a passing grade the student must

* be able to see the usefulness of quantum theory in some applications.

* know the basics of mathematical methods in physics, especially with regard to applications in quantum physics.

* have applied knowledge of some special functions.

*Skills and abilities*

For a passing grade the student must

* be able to carry out calculations in which the mathematical methods of physics are applied to problems from nanophysics.

* be able to apply the mathematical methods of the course for carrying out a computer project and analyze the results.

**Contents**

Quantum mechanics: Formalism of quantum mechanics: The Schrödinger equation as eigenvalue equation. Hermitian operators representing physical quantities, eigenvalues and eigenfunctions. The harmonic oscillator. Calculation Methodology: First order perturbation theory, variational methods and matrix diagonalization. Spherical coordinates and angular momentum. Applications to the hydrogen atom and atomic structure. Spin and magnetic interactions. Periodic potential. Bloch wave functions.

Mathematical Methods: Partial differential equations - classification and boundary conditions. General information on the eigenfunctions of operators. Bessel functions. Applications to cylindrical symmetry problems. Legendre polynomials. Spherical harmonic functions.

**Literature**

Gunnar Ohlén: Kvantvärldens fenomen, chap. 5-8

Peter S. Riseborough: Mathematical methods 1, chap. 1-9. http://www.math.temple.edu/~prisebor/mm1.pdf (available free of charge on the net)