Tilo Stroh

Scattering in Three Dimensions

Radial scattering wave functions. Boundary and continuity conditions. Solutions for step potentials. Scattering of plane harmonic waves. Scattering matrix element. Partial scattering amplitude. Scattered wave as sum over partial waves. Scattering amplitude as sum over partial scattering amplitudes. Differential cross section. Total cross section. Partial cross sections. Scattering amplitude and phase. Unitarity and the Argand diagram.

A Systematic Guide to IQ

We assume here that IQ is fully installed on your computer and that the IQ symbol featuring the letter ħ is displayed on the computers desktop. (See Appendix B for installing IQ and the file ReadMe.txt on the CD-ROM for the case that the IQ symbol is not present on the desktop.) You start IQ simply by clicking (once or twice – depending on your operating system) on that symbol. The IQ main frame appears on the desktop. It contains the main toolbar, Fig. A.1.

How to Install IQ

The CD-R essentially contains three items: It contains the program package INTERQUANTA, version 4.0. The program needs the Java Runtime Environment including Swing classes, i.e., preferably version 1.3 or higher, which, most probably, is present on your machine. If it is not, it can, in most cases, be installed on your machine from the CD-ROM as part of the installation of INTERQUANTA. For details see Sect. B.2.2 below. To display help information INTERQUANTA uses a special version of the Adobe Acrobat® Reader which runs under Java. This particular reader is also installed on your machine from the CD-ROM as part of the installation of INTERQUANTA.

Bound States in One Dimension

Introduction of the time-dependent and stationary Schrodinger equations. Computation of eigenfunctions and eigenvalues in the infinitely deep square-well potential, in the harmonic-oscillator potential and in the general step potential. Motion of a wave packet in the deep square-well potential and in the harmonic-oscillator potential.

Bound States in Three Dimensions

Introduction of the Schrodinger equation with potential. Partial wave decomposition. Spherical harmonics as eigenfunctions of angular momenta. Radial Schrodinger equation. Centrifugal barrier. Normalization and orthogonality of bound state wave functions. Infinitely deep square-well potential. Spherical step potential. Harmonic oscillator. Coulomb potential. Harmonic particle motion.

Additional Material and Hints for the Solution of Exercises

Every physical quantity q can be expressed as a product of a dimensionless numerical value qN u and its unit q u ,

Free Particle Motion in Three Dimensions

q = q{\rm N}_{u}{\rm q}_u

Spin and Magnetic Resonance

(12.1) .