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Full Description
The most up-to-date access to elementary quantum mechanics. Based on the interactive program Interquanta and its extensive 3D colour graphic features, the course guides its readers through computer experiments covering all aspects of quantum mechanics. A wide variety of more than 250 detailed, class-tested problems, provide students with unique practical experience in using such hard-to-visualise concepts as complex amplitudes, eigenvalues, and scattering cross sections. This 3rd edition includes three program versions: one requiring a coprocessor, one that can run without it, and a third program version optimised for 32-bit processors. For lecturers and teachers looking for excellent, hands-on classroom demonstrations for their quantum mechanics course.
Contents
1. Introduction.- 1.1 Interquanta.- 1.2 The Structure of this Book.- 1.3 The Demonstrations.- 1.4 The Computer Laboratory.- 1.5 Literature.- 2. Free Particle Motion in One Dimension.- 2.1 Physical Concepts.- 2.1.1 Planck's Constant. Schrodinger's Equation for a Free Particle.- 2.1.2 The Wave Packet. Group Velocity. Normalization.- 2.1.3 Analogies in Optics.- 2.2 A First Session with the Computer.- 2.2.1 Starting IQ.- 2.2.2 An Automatic Demonstration.- 2.2.3 A First Dialogue.- 2.2.4 A Little Systematics.- 2.3 The Time Development of a Gaussian Wave Packet.- 2.4 The Spectral Function of a Gaussian Wave Packet.- 2.5 The Wave Packet as a Sum of Harmonic Waves.- 2.6 Exercises.- 3. Bound States in One Dimension.- 3.1 Physical Concepts.- 3.1.1 Schrodinger's Equation with a Potential. Eigenfunctions. Eigenvalues.- 3.1.2 Normalization. Discrete Spectra. Orthonormality.- 3.1.3 The Infinitely Deep Square-Well Potential.- 3.1.4 The Harmonic Oscillator.- 3.1.5 The Step Potential.- 3.1.6 Time-Dependent Solutions.- 3.1.7 Harmonic Particle Motion. Coherent States. Squeezed States.- 3.1.8 Particle Motion in a Deep Square Well.- 3.2 Eigenstates in the Infinitely Deep Square-Well Potential and in the Harmonic-Oscillator Potential.- 3.3 Eigenstates in the Step Potential.- 3.4 Harmonic Particle Motion.- 3.5 Particle Motion in the Infinitely Deep Square-Well Potential.- 3.6 Exercises.- 4. Scattering in One Dimension.- 4.1 Physical Concepts.- 4.1.1 Stationary Scattering States. Continuum Eigenstates and Eigenvalues. Continuous Spectra.- 4.1.2 Time-Dependent Solutions of the Schrodinger Equation.- 4.1.3 Right-Moving and Left-Moving Stationary Wavesof a Free Particle.- 4.1.4 Orthogonality and Continuum Normalization of Stationary Waves of a Free Particle. Completeness.- 4.1.5 Boundary Conditions for Stationary Scattering Solutions in Step Potentials.- 4.1.6 Stationary Scattering Solutions in Step Potentials.- 4.1.7 Constituent Waves.- 4.1.8 Normalization of Continuum Eigenstates.- 4.1.9 Harmonic Waves in a Step Potential.- 4.1.10 Time-Dependent Scattering Solutions in a Step Potential.- 4.1.11 Transmission and Reflection. Unitarity. The Argand Diagram.- 4.1.12 The Tunnel Effect.- 4.1.13 Resonances.- 4.1.14 Phase Shifts upon Reflection at a Steep Rise or Deep Fall of the Potential.- 4.1.15 Transmission Resonances upon Reflection at "More- and Less-Dense Media".- 4.1.16 The Quantum-Well Device and the Quantum-Effect Device.- 4.2 Stationary Scattering States in the Step Potential.- 4.3 Scattering of a Harmonic Wave by the Step Potential.- 4.4 Scattering of a Wave Packet by the Step Potential.- 4.5 Transmission and Reflection. The Argand Diagram.- 4.6 Exercises.- 4.7 Analogies in Optics.- 4.8 Reflection and Refraction of Stationary Electromagnetic Waves.- 4.9 Reflection and Refraction of a Harmonic Light Wave.- 4.10 Scattering of a Wave Packet of Light.- 4.11 Transmission, Reflection and Argand Diagram for a Light Wave.- 4.12 Exercises.- 5. A Two-Particle System: Coupled Harmonic Oscillators.- 5.1 Physical Concepts.- 5.1.1 The Two-Particle System.- 5.1.2 Initial Condition for Distinguishable Particles.- 5.1.3 Time-Dependent Wave Functions and Probability Distributions for Distinguishable Particles.- 5.1.4 Marginal Distributions for Distinguishable Particles.- 5.1.5 Wave Functions for Indistinguishable Particles. Symmetrization for Bosons. Antisymmetrization for Fermions.- 5.1.6 Marginal Distributions of the Probability Densities of Bosons and Fermions.- 5.1.7 Normal Oscillations.- 5.2 Stationary States.- 5.3 Time Dependence of Global Quantities.- 5.4 Joint Probability Densities.- 5.5 Marginal Distributions.- 5.6 Exercises.- 6. Free Particle Motion in Three Dimensions.- 6.1 Physical Concepts.- 6.1.1 The Schrodinger Equation of a Free Particle in Three Dimensions. The Momentum Operator.- 6.1.2 The Wave Packet. Group Velocity. Normalization. The Probability Ellipsoid.- 6.1.3 Angular Momentum. Spherical Harmonics.- 6.1.4 The Stationary Schrodinger Equation in Polar Coordinates. Separation of Variables. Spherical Bessel Functions. Continuum Normalization. Completeness.- 6.1.5 Partial-Wave Decomposition of the Plane Wave.- 6.1.6 Partial-Wave Decomposition of the Gaussian Wave Packet.- 6.2 The 3D Harmonic Plane Wave.- 6.2.1 A Cartesian 3D Plot.- 6.2.2 A Polar 3D Plot.- 6.3 The Plane Wave Decomposed into Spherical Waves.- 6.4 The 3D Gaussian Wave Packet.- 6.5 The Probability Ellipsoid.- 6.6 Angular-Momentum Decomposition of a Wave Packet.- 6.7 Exercises.- 7. Bound States in Three Dimensions.- 7.1 Physical Concepts.- 7.1.1 The Schrodinger Equation for a Particle under the Action of a Force. The Centrifugal Barrier. The Effective Potential.- 7.1.2 Bound States. Scattering States. Discrete and Continuous Spectra.- 7.1.3 The Infinitely Deep Square-Well Potential.- 7.1.4 The Spherical Step Potential.- 7.1.5 The Harmonic Oscillator.- 7.1.6 The Coulomb Potential. The Hydrogen Atom.- 7.1.7 Harmonic Particle Motion.- 7.2 Radial Wave Functions in Simple Potentials.- 7.3 Radial Wave Functions in the Step Potential.- 7.4 Probability Densities.- 7.5 Harmonic Particle Motion.- 7.6 Exercises.- 8. Scattering in Three Dimensions.- 8.1 Physical Concepts.- 8.1.1 Radial Scattering Wave functions.- 8.1.2 Boundary and Continuity Conditions. Solution of the System of Inhomogeneous Linear Equations for the Coefficients.- 8.1.3 Scattering of a Plane Harmonic Wave.- 8.1.4 Scattering Amplitude and Phase. Unitarity. The Argand Diagram.- 8.2 Radial Wave functions.- 8.3 Stationary Wave Functions and Scattered Waves.- 8.4 Differential Cross Sections.- 8.5 Scattering Amplitude. Phase Shift. Partial and Total Cross Sections.- 8.6 Exercises.- 9. Special Functions of Mathematical Physics.- 9.1 Basic Formulae.- 9.1.1 Hermite Polynomials.- 9.1.2 Harmonic-Oscillator Eigenfunctions.- 9.1.3 Legendre Polynomials and Legendre functions.- 9.1.4 Spherical Harmonics.- 9.1.5 Bessel functions.- 9.1.6 Spherical Bessel functions.- 9.1.7 Laguerre Polynomials.- 9.1.8 Radial Eigenfunctions of the Harmonic Oscillator.- 9.1.9 Radial Eigenfunctions of the Hydrogen Atom.- 9.2 Hermite Polynomials.- 9.3 Eigenfunctions of the One-Dimensional Harmonic Oscillator.- 9.4 Legendre Polynomials and Associated Legendre functions.- 9.4.1 Type 2 Plots-Functions of x or cos ?.- 9.4.2 Type 2 Plots-Polar Diagrams.- 9.5 Spherical Harmonics.- 9.6 Bessel functions.- 9.6.1 Type 2 Plots.- 9.6.2 Type 0 Plots.- 9.7 Spherical Bessel functions.- 9.8 Laguerre Polynomials.- 9.8.1 Type 2 Plots.- 9.8.2 Type 0 Plots.- 9.9 Radial Eigenfunctions of the Harmonic Oscillator.- 9.10 Radial Eigenfunctions of the Hydrogen Atom.- 9.11 Simple Functions of a Complex Variable.- 9.12 Exercises.- 10. Additional Material and Hints for the Solution of Exercises.- 10.1 Units and Orders of Magnitude.- 10.1.1 Definitions.- 10.1.2 SI Units.- 10.1.3 Scaled Units.- 10.1.4 Atomic and Subatomic Units.- 10.1.5 Data-Table Units.- 10.1.6 Special Scales.- 10.2 Argand Diagrams and Unitarity for One-Dimensional Problems.- 10.2.1 Probability Conservation and the Unitarity of the Scattering Matrix.- 10.2.2 Time Reversal and the Scattering Matrix.- 10.2.3 Diagonalization of the Scattering Matrix.- 10.2.5 Resonances.- 10.3 Hints and Answers to the Exercises.- Appendix A. A Systematic Guide to IQ.- A.1 Dialog Between the User and IQ.- A.1.1 A Simple Example.- A.1.2 The General Form of Commands.- A.1.3 The Descriptor File.- A.1.4 The Descriptor (Record).- A.1.5 The PLOT Command.- A.1.6 The STOP Command.- A.1.7 HELP: The Commands HE and PH.- A.2 Coordinate Systems and Transformations.- A.2.1 The Different Coordinate Systems.- A.2.2 Defining the Transformations.- A.3 The Different Types of Plot.- A.3.1 Choosing a Plot Type: The Command CH.- A.3.2 Cartesian 3D Plots (Type 0 Plots).- A.3.3 Polar 3D Plots (Type 1 Plots).- A.3.4 2D Plots (Type 2 Plots).- A.3.5 3D Column Plots (Type 3 Plots).- A.3.6 Special 3D Plots (Type 10 Plots).- A.4 The Background in the Plots.- A.4.1 Boxes and Coordinate Axes: The Command BO.- A.4.2 Scales.- A.4.3 Arrows.- A.4.4 Text and Numbers.- A.4.5 Mathematical Symbols and Formulae.- A.5 Further Commands.- A.5.1 Line Styles.- A.5.2 Multiple Plots.- A.5.3 Combined Plots.- A.5.4 Using Different Plotting Devices.- A.5.5 The Different Running Modes.- A.5.6 Definition of Physical Variables: The Commands V0 to V9.- A.5.7 Reserved Commands.- Appendix B. How to Install IQ.- B.1 Hardware Requirements.- B.2 Operating-System Requirements.- B.3 Diskette Format.- B.4 Installation.- B.5 Reformatting IQ for Different Types of Diskette.- Appendix C. Lists of All Files Provided.- C.1 Command Files.- C.2 Program Files.- C.3 Descriptor Files for Examples and Exercises.- C.4 Command Input Files and Associated Descriptor Files for Demonstrations.- C.5 DataFiles.- C.6 HelpFiles.- Appendix D. Graphics Devices and Metafiles.- Index of IQ Commands.
