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Thaller B. — Visual quantum mechanics
Thaller B. — Visual quantum mechanics

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Название: Visual quantum mechanics

Автор: 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: en

Рубрика: Физика/Квантовая механика/Учебники/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 283

Добавлена в каталог: 02.10.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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