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Thaller B. — Visual quantum mechanics
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Название: Visual quantum mechanicsАвтор: Thaller B. Аннотация: The use of visualization techniques greatly enhances the understanding of quantum mechanics as it allows us to depict phenomena that cannot be seen by any other means. "Visual Quantum Mechanics" uses the computer generated animations found on the accompanying CD-ROM to introduce, motivate, and illustrate the concepts explained in the book. For example, by watching QuickTime movies of the solutions of Schroedinger's equation, students will be able to develop a feeling for the behavior of quantum mechanical systems that cannot be gained by conventional means. While there are other books on the market that use Mathematica and Maple to teach quantum mechanics, this book differs in that the text describes the mathematical and physical ideas of quantum mechanics in the conventional manner, with no special emphasis on computational physics or the requirement that the reader know a symbolic computation package or Mathematica. In this book, instead, the computer is used to provide easy access to a large collection of animated illustrations, interactive pictures, and lots of supplementary materials. "Visual Quantum Mechanics" takes a mathematical rather than a physical approach to quantum mechanics, and includes results more typical in more advanced books but which are more comprehensible via visualization. Despite the presentations of advanced results, the book requires only calculus, and the book will fill the gap between classical quantum mechanics texts and mathematically advanced books. The book will have a home page at the author's institution (http://www.kfunigraz.ac.at/imawww/vqm/) which will include supplementary material, exercises and solutions, additional animations, and links to other sites with quantum mechanical visualization. This book along with its accompanying CD-ROM, which contains over 300 digital movies, form a complete introductory course on spinless particles in one and two dimensions. There is a second book in development which will cover such topics as spherical symmetry in three dimensions, the hydrogen atom, scattering theory and resonances, periodic potentials, particles with spin, an relativistic problems (the Dirac equation).
Язык: Рубрика: Физика /Квантовая механика /Учебники /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1999Количество страниц: 283Добавлена в каталог: 02.10.2005Операции: Положить на полку |
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Предметный указатель
Absolute value 3 action 51 Adjoint 143 Aharonov — Bohm effect 202 Airy functions 197 Amplitude 18 56 Amplitude function 57 Annihilation operator 183 Argument 3 Asymptotic time evolution 75 236 Avron — Herbst formula 193 Basis 24 Basis of eigenfunctions 118 164 Bohm’s quantum mechanics 72 Bouncing ball 196 Bound states 118 159 Boundary condition 108 Boundary condition, Dirichlet 108 197 Boundary condition, Neumann 110 Boundary condition, periodic 124 Bounded 31 box 111 Bragg condition 52 Brightness 5 Canonical commutation relations 93 151 180 210 Canonically conjugate 204 Cauchy sequence 23 Cauchy — Schwarz inequality 23 41 Center of motion 208 214 Characteristic function 19 100 CIE-Lab 8 Classical motion, harmonic oscillator 159 166 173 181 Classical motion, linear potential 192 Classical motion, magnetic field 207 Classically allowed region 159 Closure 32 Coherent states 175 184 Collapse of wave packet 102 Color manifold 5 Color map 7 Commensurable 199 Commutator 30 93 151 Commuting operators 149 153 Compactified complex plane 4 Compatible 70 153 Completeness 23 Completeness of oscillator functions 186 Completeness property 24 complex infinity 4 Complex number 2 Complex plane 3 Composition of linear operators 30 Confluent hypergeometric function 223 Conservation law 154 Conservation of the norm 62 Constant force 192 Constant magnetic field 202 224 Constant of motion 154 172 Constant potential 98 Constants of motion 210 Continuity at zero 32 Continuity equation 71 continuous 31 Convergence in the mean 18 119 Coulomb gauge 99 Crank — Nicolson formula 260 Creation operator 183 Current vector 71 Degeneracy 115 Delta distribution 46 Dense set 32 Derivative 36 Determinative measurement 69 Dimensionless units 161 Dirac delta function 45 Dirichlet boundary condition 108 141 145 197 233 dispersion relation 50 Distance 22 distribution 46 Domain 30 Domain, extension of 32 Dualism 50 Eigenfunction 115 Eigenfunction, expansion 118 163 Eigenspace 115 Eigenvalues 115 142 221 Eigenvalues, box 116 124 Eigenvalues, harmonic oscillator 164 Eigenvalues, linear potential 198 Eigenvalues, magnetic field 205 Eigenvector 115 142 Einstein relations 51 Elastic reflection 110 196 electric field 95 Electric field, homogeneous 192 Elementary experiment 67 126 Energy representation 81 89 90 139 234 Energy spectrum 224 Equilibrium 159 Essentially self-adjoint 146 Euler method 261 Euler’s formula 3 Even function 252 Event 130 Evolution equation 84 expectation value 68 89 Expectation value, momentum 43 Expectation value, position 43 Expectation value, time evolution 172 Exponential operator 184 Fourier inversion theorem 28 Fourier series 18 25 56 Fourier space 27 Fourier sum 16 Fourier transform 26 180 Fourier transform, of a Gaussian 39 Fourier transform, of oscillator states 170 Fourier transform, unitarity 139 Fourier transformation, distributional 46 Fourier transformation, inverse 27 Fourier transformation, one-dimensional 26 Fourier transformation, several variables 27 Fourier — Plancherel theorem 29 Free fall 192 frequency 50 Function, complex-valued 9 Function, square-integrable 17 Functions, delta function 45 Functions, test functions 46 Gauge field 99 Gauge freedom 98 Gauge transformation 98 139 Gaussian function 38 Gaussian function, free time evolution 60 Gaussian initial function 176 Generalized derivative 36 Generator 139 Generator of rotations 219 Gibbs’ phenomenon 19 Glauber form 186 Graph 9 Gravitational field 192 Ground state 124 182 Hamiltonian 94 135 Hardy’s inequality 45 harmonic oscillator 157 205 222 Harmonic oscillator in two dimensions 177 Heisenberg equation 172 195 Heisenberg’s uncertainty relation 41 Hermite function 164 Hermite polynomial 164 Hermitian 90 Hidden variable 68 72 133 Hilbert space 17 21—25 HLS color system 5 HSB color system 5 Idempotent 100 Imaginary part 3 Incoming wave 230 Independent events 134 Inequalities 44 Infinite degeneracy 212 225 Infinitesimal generator 139 Initial function 59 Initial-value problem 59 140 167 Interference 86 Interpretation, wave function 63 Invariance 153 Invariance, of the norm 62 Invariance, under reflections 251 Invariance, under rotations 219 Invariance, under translations 212 Inverse Fourier transformation 27 Isometric operator 138 kinetic energy 88 Kummer’s equation 223 Ladder operators 183 Laplace operator 53 88 221 Lightness 6 linear combination 16 22 Linear functional 46 Linear operator 30 Linear operator, boundedness 31 Linear operator, closure 32 Linear operator, composition 30 Linear operator, continuity 31 Linear operator, domain 30 Linear operator, functions 37 Linear operator, norm 31 Linear operator, product 30 Linear operator, unbounded 31 Linear potential 192 Linear space 21 Linearly independent 24 Long-time behavior 72 Lorentz force 208 Magnetic field 96 200 Magnetic field, constant field 202 Magnetic field, field strength 201 Magnetic field, translations 211 Magnetic field:energy eigenvalues 205 Mean value 43 68 Measurement process 67 69 80 101 Mehler kernel 187 217 Method of mirrors 109 Mild solution 138 Mixed state 67 Modulus 3 Momentum distribution 58 Momentum operator 88 Momentum space 27 54 170 Multiplicity 115 Neumann boundary condition 110 Noether’s theorem 154 Noncommutativity 30 149 Nondegenerate 124 Norm 22 31 Normalization condition 64 Numerical solution 257 Observable 86 115 Observable, expectation value 89 Observable, uncertainty 90 Odd function 118 252 One-parameter unitary group 139 Operator, adjoint 143 Operator, Hamiltonian 94 Operator, self-adjoint 144 Operator, symmetric 90 141 Operator, unitary 138 Orthogonal 24 Orthonormal basis of oscillator states 165 Orthonormal set 21 24 Oscillator frequency 158 Outgoing wave 230 Parity transformation 251 Particle 50 Pauli matrices 14 Period 50 120 169 Periodic boundary conditions 124 Periodic function 16 Periodic time dependence 120 169 Phase 3 50 Phase factor 97 Phase shift 34 Phase space 84 179 phase velocity 50 98 photoelectric effect 50 51 Photon 51 Pilot wave theory 72 Planck’s constant 51 Plane wave 50 109 115 229 Plane wave, stationary 16 Poincare gauge 99 202 Poisson bracket 93 Polar coordinates 220 Polar form 3 Position operator 86 Position probability, classical 167 Position space 27 Potential barrier 243 potential energy 91 potential step 231 Potential well 248 Potential, asymptotically constant 228 Preparation of state 67 70 Preparatory measurement 70 Probability space 130 Projection operator 101 Projection postulate 102 Property 101 Pure state 67 104 Quasi-periodic 56 199 Real part 3 Reflection 110 Reflection, coefficient 232 Reflection, probability 232 Reflection, symmetry 251 Regular distribution 46 Relativistic energy operator 37 Resolvent 38 Resonance 244 RGB color system 5 Riemann zeta function 13 Riemann — Lebesgue lemma 28 Rotation 218 Saturation 5 Scalar potential 95 Scalar product 22 Scaling transformation 34 53 139 161 Scanning tunneling microscope 248 Scattering matrix 240 Scattering operator 240 Scattering theory 227 Schrodinger cat 78 Schrodinger cat state 125 Schrodinger equation in an electric field 95 Schrodinger equation, free particles 53 Schrodinger equation, linearity 56 Schrodinger equation, nonuniqueness 98 Schrodinger equation, stationary 117
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