Quantum Mechanics Using Maple ®

Upper-year undergraduate and beginning graduate students in physics who want to become acquainted with solving quantum mechanical problems by using Maple will welcome this book that fills a gap. All worksheets were tested under Maple V release 3 running under Windows. They are provided on a diskette readable by IBM -compatible, Macintosh , and UNIX computers.

Klappentext

Quantum Mechanics Using Maple permits the study of quantum mechanics in a novel, interactive way using the computer algebra and graphics system Maple V. Usually the physics student is distracted from understanding the concepts of modern physics by the need to master unfamiliar mathematics at the same time. In 39 guided Maple sessions the reader explores many standard quantum mechanics problems, as well as some advanced topics that introduce approximation techniques. A solid knowledge of Maple V is acquired as it applies to advanced mathematics relevant for engineering, physics, and applied mathematics. The diskette contains 39 Maple V for Windows worksheet files to reproduce all the problems presented in the text. The suggested exercises can be performed with a minimum of typing.

Inhalt

1. Problems in One Dimension.- 1.1 Introduction.- 1.2 Harmonic Oscillator.- 1.3 A Time-Dependent Problem.- 1.4 Variational Method.- 1.5 Commutation Relations.- 1.6 Anharmonic Oscillator.- 2. Bound States in 1D.- 2.1 Local Energy.- 2.2 External Source.- 2.3 Periodic Lattice.- 2.4 Lanczos Tridiagonalization.- 2.5 Shooting Method.- 2.6 Discrete Space.- 3. Scattering in 1D.- 3.1 Wavepackets.- 3.2 Potential Well and Barrier.- 3.3 Tunneling Ionization.- 3.4 Alpha Decay.- 3.5 Motion Picture.- 4. Problems in 3D.- 4.1 Angular Momentum.- 4.2 Radial Equation.- 4.3 Atomic Model.- 4.4 Zeeman Splitting.- 4.5 DC Stark Effect.- 5. Spin and Time-Dependent Processes.- 5.1 Pauli Equation.- 5.2 Magnetic Moments.- 5.3 Temporary Perturbation.- 5.4 Collisional Excitation.- 6. Scattering in 3D.- 6.1 Partial Waves.- 6.2 Potential Scattering.- 6.3 Born Approximation.- 6.4 Variational Method.- 7. Many-Particle Problems.- 7.1 Helium Atom.- 7.2 Hydrogen Molecule.- 7.3 Vibrating Molecules.- 7.4 Angular-Momentum Coupling.- 7.5 Two-Particle Correlations.- 8. Special Functions.- 8.1 Hermite Polynomials.- 8.2 Laguerre Polynomials.- 8.3 Legendre Polynomials.- 8.4 Coulomb Waves.- References.