Quantum Mechanics Using Maple ®

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.

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.