1000 Solved Problems in Modern Physics

1. Auflage 2010
ISBN: 978-3-642-04333-8
Verlag: Springer
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 634 Seiten

This book is targeted mainly to the undergraduate students of USA, UK and other European countries, and the M. Sc of Asian countries, but will be found useful for the graduate students, Graduate Record Examination (GRE), Teachers and Tutors. This is a by-product of lectures given at the Osmania University, University of Ottawa and University of Tebrez over several years, and is intended to assist the students in their assignments and examinations. The book covers a wide spectrum of disciplines in Modern Physics, and is mainly based on the actual examination papers of UK and the Indian Universities. The selected problems display a large variety and conform to syllabi which are currently being used in various countries. The book is divided into ten chapters. Each chapter begins with basic concepts containing a set of formulae and explanatory notes for quick reference, followed by a number of problems and their detailed solutions. The problems are judiciously selected and are arranged section-wise. The so- tions are neither pedantic nor terse. The approach is straight forward and step-- step solutions are elaborately provided. More importantly the relevant formulas used for solving the problems can be located in the beginning of each chapter. There are approximately 150 line diagrams for illustration. Basic quantum mechanics, elementary calculus, vector calculus and Algebra are the pre-requisites.

Autoren/Hrsg.

Inhaltsverzeichnis

1;Preface;6
2;Contents;9
3;1 Mathematical Physics;15
3.1;1.1 Basic Concepts and Formulae;15
3.2;1.2 Problems;35
3.2.1;1.2.1 Vector Calculus;35
3.2.2;1.2.2 Fourier Series and Fourier Transforms;36
3.2.3;1.2.3 Gamma and Beta Functions;37
3.2.4;1.2.4 Matrix Algebra;38
3.2.5;1.2.5 Maxima and Minima;38
3.2.6;1.2.6 Series;39
3.2.7;1.2.7 Integration;39
3.2.8;1.2.8 Ordinary Differential Equations;40
3.2.9;1.2.9 Laplace Transforms;43
3.2.10;1.2.10 Special Functions;43
3.2.11;1.2.11 Complex Variables;44
3.2.12;1.2.12 Calculus of Variation;45
3.2.13;1.2.13 Statistical Distributions;46
3.2.14;1.2.14 Numerical Integration;47
3.3;1.3 Solutions;47
3.3.1;1.3.1 Vector Calculus;47
3.3.2;1.3.2 Fourier Series and Fourier Transforms;53
3.3.3;1.3.3 Gamma and Beta Functions;56
3.3.4;1.3.4 Matrix Algebra;58
3.3.5;1.3.5 Maxima and Minima;62
3.3.6;1.3.6 Series;63
3.3.7;1.3.7 Integration;65
3.3.8;1.3.8 Ordinary Differential Equations;71
3.3.9;1.3.9 Laplace Transforms;81
3.3.10;1.3.10 Special Functions;82
3.3.11;1.3.11 Complex Variables;86
3.3.12;1.3.12 Calculus of Variation;88
3.3.13;1.3.13 Statistical Distribution;91
3.3.14;1.3.14 Numerical Integration;99
4;2 Quantum Mechanics -- I ;101
4.1;2.1 Basic Concepts and Formulae;101
4.2;2.2 Problems;106
4.2.1;2.2.1 de Broglie Waves;106
4.2.2;2.2.2 Hydrogen Atom;106
4.2.3;2.2.3 X-rays;109
4.2.4;2.2.4 Spin and µ Quantum Numbers -- Stern--Gerlah's Experiment;110
4.2.5;2.2.5 Spectroscopy;111
4.2.6;2.2.6 Molecules;113
4.2.7;2.2.7 Commutators;114
4.2.8;2.2.8 Uncertainty Principle;115
4.3;2.3 Solutions;115
4.3.1;2.3.1 de Broglie Waves;115
4.3.2;2.3.2 Hydrogen Atom;117
4.3.3;2.3.3 X-rays;122
4.3.4;2.3.4 Spin and µ Quantum Numbers -- Stern--Gerlah's Experiment;125
4.3.5;2.3.5 Spectroscopy;129
4.3.6;2.3.6 Molecules;134
4.3.7;2.3.7 Commutators;137
4.3.8;2.3.8 Uncertainty Principle;142
5;3 Quantum Mechanics -- II;145
5.1;3.1 Basic Concepts and Formulae;145
5.2;3.2 Problems;151
5.2.1;3.2.1 Wave Function;151
5.2.2;3.2.2 Schrodinger Equation;152
5.2.3;3.2.3 Potential Wells and Barriers;154
5.2.4;3.2.4 Simple Harmonic Oscillator;160
5.2.5;3.2.5 Hydrogen Atom;161
5.2.6;3.2.6 Angular Momentum;163
5.2.7;3.2.7 Approximate Methods;166
5.2.8;3.2.8 Scattering (Phase-Shift Analysis);167
5.2.9;3.2.9 Scattering (Born Approximation);168
5.3;3.3 Solutions;170
5.3.1;3.3.1 Wave Function;170
5.3.2;3.3.2 Schrodinger Equation;176
5.3.3;3.3.3 Potential Wells and Barriers;182
5.3.4;3.3.4 Simple Harmonic Oscillator;213
5.3.5;3.3.5 Hydrogen Atom;223
5.3.6;3.3.6 Angular Momentum;229
5.3.7;3.3.7 Approximate Methods;243
5.3.8;3.3.8 Scattering (Phase Shift Analysis);247
5.3.9;3.3.9 Scattering (Born Approximation);254
6;4 Thermodynamics and Statistical Physics ;261
6.1;4.1 Basic Concepts and Formulae;261
6.2;4.2 Problems;265
6.2.1;4.2.1 Kinetic Theory of Gases;265
6.2.2;4.2.2 Maxwell's Thermodynamic Relations;267
6.2.3;4.2.3 Statistical Distributions;269
6.2.4;4.2.4 Blackbody Radiation;270
6.3;4.3 Solutions;272
6.3.1;4.3.1 Kinetic Theory of Gases;272
6.3.2;4.3.2 Maxwell's Thermodynamic Relations;280
6.3.3;4.3.3 Statistical Distributions;293
6.3.4;4.3.4 Blackbody Radiation;299
7;5 Solid State Physics ;305
7.1;5.1 Basic Concepts and Formulae;305
7.2;5.2 Problems;308
7.2.1;5.2.1 Crystal Structure;308
7.2.2;5.2.2 Crystal Properties;308
7.2.3;5.2.3 Metals;309
7.2.4;5.2.4 Semiconductors;311
7.2.5;5.2.5 Superconductor;312
7.3;5.3 Solutions;313
7.3.1;5.3.1 Crystal Structure;313
7.3.2;5.3.2 Crystal Properties;315
7.3.3;5.3.3 Metals;317
7.3.4;5.3.4 Semiconductors;323
7.3.5;5.3.5 Superconductor;325
8;6 Special Theory of Relativity ;327
8.1;6.1 Basic Concepts and Formulae;327
8.2;6.2 Problems;333
8.2.1;6.2.1 Lorentz Transformations;333
8.2.2;6.2.2 Length, Time, Velocity;334
8.2.3;6.2.3 Mass, Momentum, Energy;337
8.2.4;6.2.4 Invariance Principle;340
8.2.5;6.2.5 Transformation of Angles and Doppler Effect;342
8.2.6;6.2.6 Threshold of Particle Production;344
8.3;6.3 Solutions;346
8.3.1;6.3.1 Lorentz Transformations;346
8.3.2;6.3.2 Length, Time, Velocity;352
8.3.3;6.3.3 Mass, Momentum, Energy;356
8.3.4;6.3.4 Invariance Principle;365
8.3.5;6.3.5 Transformation of Angles and Doppler Effect;369
8.3.6;6.3.6 Threshold of Particle Production;379
9;7 Nuclear Physics -- I ;382
9.1;7.1 Basic Concepts and Formulae;382
9.2;7.2 Problems;395
9.2.1;7.2.1 Kinematics of Scattering;395
9.2.2;7.2.2 Rutherford Scattering;396
9.2.3;7.2.3 Ionization, Range and Straggling;398
9.2.4;7.2.4 Compton Scattering;400
9.2.5;7.2.5 Photoelectric Effect;401
9.2.6;7.2.6 Pair Production;403
9.2.7;7.2.7 Cerenkov Radiation;403
9.2.8;7.2.8 Nuclear Resonance;403
9.2.9;7.2.9 Radioactivity (General);404
9.2.10;7.2.10 Alpha-Decay;406
9.2.11;7.2.11 Beta-Decay;406
9.3;7.3 Solutions;407
9.3.1;7.3.1 Kinematics of Scattering;407
9.3.2;7.3.2 Rutherford Scattering;412
9.3.3;7.3.3 Ionization, Range and Straggling;417
9.3.4;7.3.4 Compton Scattering;420
9.3.5;7.3.5 Photoelectric Effect;424
9.3.6;7.3.6 Pair Production;427
9.3.7;7.3.7 Cerenkov Radiation;428
9.3.8;7.3.8 Nuclear Resonance;429
9.3.9;7.3.9 Radioactivity (General);430
9.3.10;7.3.10 Alpha-Decay;435
9.3.11;7.3.11 Beta-Decay;436
10;8 Nuclear Physics -- II ;439
10.1;8.1 Basic Concepts and Formulae;439
10.2;8.2 Problems;446
10.2.1;8.2.1 Atomic Masses and Radii;446
10.2.2;8.2.2 Electric Potential and Energy;447
10.2.3;8.2.3 Nuclear Spin and Magnetic Moment;447
10.2.4;8.2.4 Electric Quadrupole Moment;447
10.2.5;8.2.5 Nuclear Stability;448
10.2.6;8.2.6 Fermi Gas Model;449
10.2.7;8.2.7 Shell Model;449
10.2.8;8.2.8 Liquid Drop Model;450
10.2.9;8.2.9 Optical Model;451
10.2.10;8.2.10 Nuclear Reactions (General);452
10.2.11;8.2.11 Cross-sections;454
10.2.12;8.2.12 Nuclear Reactions via Compound Nucleus;455
10.2.13;8.2.13 Direct Reactions;455
10.2.14;8.2.14 Fission and Nuclear Reactors;456
10.2.15;8.2.15 Fusion;459
10.3;8.3 Solutions;459
10.3.1;8.3.1 Atomic Masses and Radii;459
10.3.2;8.3.2 Electric Potential and Energy;461
10.3.3;8.3.3 Nuclear Spin and Magnetic Moment;462
10.3.4;8.3.4 Electric Quadrupole Moment;463
10.3.5;8.3.5 Nuclear Stability;466
10.3.6;8.3.6 Fermi Gas Model;468
10.3.7;8.3.7 Shell Model;469
10.3.8;8.3.8 Liquid Drop Model;470
10.3.9;8.3.9 Optical Model;472
10.3.10;8.3.10 Nuclear Reactions (General);474
10.3.11;8.3.11 Cross-sections;480
10.3.12;8.3.12 Nuclear Reactions via Compound Nucleus;481
10.3.13;8.3.13 Direct Reactions;482
10.3.14;8.3.14 Fission and Nuclear Reactors;483
10.3.15;8.3.15 Fusion;495
11;9 Particle Physics -- I ;496
11.1;9.1 Basic Concepts and Formulae;496
11.2;9.2 Problems;499
11.2.1;9.2.1 System of Units;499
11.2.2;9.2.2 Production;500
11.2.3;9.2.3 Interaction;500
11.2.4;9.2.4 Decay;502
11.2.5;9.2.5 Ionization Chamber, GM Counter and Proportional Counters;504
11.2.6;9.2.6 Scintillation Counter;506
11.2.7;9.2.7 Cerenkov Counter;507
11.2.8;9.2.8 Solid State Detector;508
11.2.9;9.2.9 Emulsions;508
11.2.10;9.2.10 Motion of Charged Particles in Magnetic Field;508
11.2.11;9.2.11 Betatron;509
11.2.12;9.2.12 Cyclotron;510
11.2.13;9.2.13 Synchrotron;511
11.2.14;9.2.14 Linear Accelerator;512
11.2.15;9.2.15 Colliders;513
11.3;9.3 Solutions;514
11.3.1;9.3.1 System of Units;514
11.3.2;9.3.2 Production;515
11.3.3;9.3.3 Interaction;516
11.3.4;9.3.4 Decay;519
11.3.5;9.3.5 Ionization Chamber, GM Counter and Proportional Counters;523
11.3.6;9.3.6 Scintillation Counter;526
11.3.7;9.3.7 Cerenkov Counter;529
11.3.8;9.3.8 Solid State Detector;531
11.3.9;9.3.9 Emulsions;531
11.3.10;9.3.10 Motion of Charged Particles in Magnetic Field;532
11.3.11;9.3.11 Betatron;535
11.3.12;9.3.12 Cyclotron;535
11.3.13;9.3.13 Synchrotron;538
11.3.14;9.3.14 Linear Accelerator;541
11.3.15;9.3.15 Colliders;542
12;10 Particle Physics -- II ;545
12.1;10.1 Basic Concepts and Formulae;545
12.2;10.2 Problems;554
12.2.1;10.2.1 Conservation Laws;554
12.2.2;10.2.2 Strong Interactions;556
12.2.3;10.2.3 Quarks;560
12.2.4;10.2.4 Electromagnetic Interactions;561
12.2.5;10.2.5 Weak Interactions;562
12.2.6;10.2.6 Electro-Weak Interactions;566
12.2.7;10.2.7 Feynman Diagrams;566
12.3;10.3 Solutions;568
12.3.1;10.3.1 Conservation Laws;568
12.3.2;10.3.2 Strong Interactions;573
12.3.3;10.3.3 Quarks;582
12.3.4;10.3.4 Electromagnetic Interactions;587
12.3.5;10.3.5 Weak Interactions;588
12.3.6;10.3.6 Electro-weak Interactions;600
12.3.7;10.3.7 Feynman Diagrams;602
13;Appendix: Problem Index;613
14;Index;642