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1000 Solved Problems in Modern Physics

(Romina) #1

  • 1 Mathematical Physics............................................

    • 1.1 Basic Concepts and Formulae

    • 1.2 Problems..................................................

      • 1.2.1 VectorCalculus....................................

      • 1.2.2 FourierSeriesandFourierTransforms.................

      • 1.2.3 Gamma and Beta Functions

      • 1.2.4 Matrix Algebra

      • 1.2.5 MaximaandMinima

      • 1.2.6 Series............................................

      • 1.2.7 Integration........................................

      • 1.2.8 OrdinaryDifferentialEquations......................

      • 1.2.9 LaplaceTransforms

      • 1.2.10 Special Functions

      • 1.2.11 ComplexVariables.................................

      • 1.2.12 CalculusofVariation...............................

      • 1.2.13 StatisticalDistributions

      • 1.2.14 NumericalIntegration



    • 1.3 Solutions..................................................

      • 1.3.1 VectorCalculus....................................

      • 1.3.2 FourierSeriesandFourierTransforms.................

      • 1.3.3 Gamma and Beta Functions

      • 1.3.4 Matrix Algebra

      • 1.3.5 MaximaandMinima

      • 1.3.6 Series............................................

      • 1.3.7 Integration........................................

      • 1.3.8 OrdinaryDifferentialEquations......................

      • 1.3.9 LaplaceTransforms

      • 1.3.10 Special Functions

      • 1.3.11 ComplexVariables.................................

      • 1.3.12 CalculusofVariation...............................

      • 1.3.13 StatisticalDistribution..............................

      • 1.3.14 NumericalIntegration





  • 2 Quantum Mechanics – I xii Contents

    • 2.1 Basic Concepts and Formulae

    • 2.2 Problems..................................................

      • 2.2.1 deBroglieWaves

      • 2.2.2 Hydrogen Atom...................................

      • 2.2.3 X-rays

        • Experiment 2.2.4 Spin andμand Quantum Numbers – Stern–Gerlah’s



      • 2.2.5 Spectroscopy

      • 2.2.6 Molecules

      • 2.2.7 Commutators .....................................

      • 2.2.8 Uncertainty Principle...............................



    • 2.3 Solutions..................................................

      • 2.3.1 deBroglieWaves ..................................

      • 2.3.2 Hydrogen Atom...................................

      • 2.3.3 X-rays ...........................................

        • Experiment 2.3.4 Spin andμand Quantum Numbers – Stern–Gerlah’s



      • 2.3.5 Spectroscopy ....................................

      • 2.3.6 Molecules ....................................

      • 2.3.7 Commutators .....................................

      • 2.3.8 Uncertainty Principle...............................





  • 3 Quantum Mechanics – II.........................................

    • 3.1 Basic Concepts and Formulae ................................

    • 3.2 Problems..................................................

      • 3.2.1 Wave Function ....................................

      • 3.2.2 Schrodinger Equation. .........................

      • 3.2.3 PotentialWellsandBarriers .........................

      • 3.2.4 Simple Harmonic Oscillator .........................

      • 3.2.5 Hydrogen Atom...................................

      • 3.2.6 Angular Momentum ................................

      • 3.2.7 Approximate Methods .........................

      • 3.2.8 Scattering (Phase-Shift Analysis) .....................

      • 3.2.9 Scattering(BornApproximation).....................



    • 3.3 Solutions..................................................

      • 3.3.1 Wave Function ....................................

      • 3.3.2 Schrodinger Equation. .........................

      • 3.3.3 PotentialWellsandBarriers .........................

      • 3.3.4 Simple Harmonic Oscillator .........................

      • 3.3.5 Hydrogen Atom...................................

      • 3.3.6 Angular Momentum ................................

      • 3.3.7 Approximate Methods .........................

      • 3.3.8 Scattering (Phase Shift Analysis) .....................

      • 3.3.9 Scattering(BornApproximation).....................





  • 4 Thermodynamics and Statistical Physics .......................... Contents xiii

    • 4.1 Basic Concepts and Formulae ................................

    • 4.2 Problems..................................................

      • 4.2.1 Kinetic Theory of Gases .........................

      • 4.2.2 Maxwell’s Thermodynamic Relations ..............

      • 4.2.3 StatisticalDistributions .............................

      • 4.2.4 Blackbody Radiation...............................



    • 4.3 Solutions..................................................

      • 4.3.1 Kinetic Theory of Gases .........................

      • 4.3.2 Maxwell’s Thermodynamic Relations ..............

      • 4.3.3 StatisticalDistributions .............................

      • 4.3.4 Blackbody Radiation...............................





  • 5 Solid State Physics..............................................

    • 5.1 Basic Concepts and Formulae ................................

    • 5.2 Problems..................................................

      • 5.2.1 CrystalStructure...................................

      • 5.2.2 Crystal Properties ................................

      • 5.2.3 Metals ...........................................

      • 5.2.4 Semiconductors...................................

      • 5.2.5 Superconductor ....................................



    • 5.3 Solutions..................................................

      • 5.3.1 CrystalStructure...................................

      • 5.3.2 Crystal Properties ................................

      • 5.3.3 Metals ...........................................

      • 5.3.4 Semiconductors...................................

      • 5.3.5 Superconductor ....................................





  • 6 Special Theory of Relativity......................................

    • 6.1 Basic Concepts and Formulae ................................

    • 6.2 Problems..................................................

      • 6.2.1 LorentzTransformations............................

      • 6.2.2 Length, Time, Velocity .........................

      • 6.2.3 Mass,Momentum,Energy ..........................

      • 6.2.4 Invariance Principle ................................

      • 6.2.5 Transformation of Angles and Doppler Effect .......

      • 6.2.6 Threshold of Particle Production .....................



    • 6.3 Solutions..................................................

      • 6.3.1 LorentzTransformations............................

      • 6.3.2 Length, Time, Velocity .........................

      • 6.3.3 Mass,Momentum,Energy ..........................

      • 6.3.4 Invariance Principle ................................

      • 6.3.5 Transformation of Angles and Doppler Effect .......

      • 6.3.6 Threshold of Particle Production .....................





  • 7 Nuclear Physics – I.............................................. xiv Contents

    • 7.1 Basic Concepts and Formulae ................................

    • 7.2 Problems..................................................

      • 7.2.1 KinematicsofScattering............................

      • 7.2.2 RutherfordScattering...............................

      • 7.2.3 Ionization, Range and Straggling .....................

      • 7.2.4 ComptonScattering................................

      • 7.2.5 Photoelectric Effect ................................

      • 7.2.6 Pair Production ....................................

      • 7.2.7 CerenkovRadiation ................................

      • 7.2.8 Nuclear Resonance ................................

      • 7.2.9 Radioactivity (General) .........................

      • 7.2.10 Alpha-Decay ....................................

      • 7.2.11 Beta-Decay ....................................



    • 7.3 Solutions..................................................

      • 7.3.1 KinematicsofScattering............................

      • 7.3.2 RutherfordScattering...............................

      • 7.3.3 Ionization, Range and Straggling .....................

      • 7.3.4 ComptonScattering................................

      • 7.3.5 Photoelectric Effect ................................

      • 7.3.6 Pair Production ....................................

      • 7.3.7 CerenkovRadiation ................................

      • 7.3.8 Nuclear Resonance ................................

      • 7.3.9 Radioactivity (General) .........................

      • 7.3.10 Alpha-Decay ....................................

      • 7.3.11 Beta-Decay ....................................





  • 8 Nuclear Physics – II.............................................

    • 8.1 Basic Concepts and Formulae ................................

    • 8.2 Problems..................................................

      • 8.2.1 AtomicMassesandRadii ...........................

      • 8.2.2 ElectricPotentialandEnergy ........................

      • 8.2.3 Nuclear Spin and Magnetic Moment ..............

      • 8.2.4 Electric Quadrupole Moment........................

      • 8.2.5 Nuclear Stability...................................

      • 8.2.6 Fermi Gas Model ................................

      • 8.2.7 Shell Model ....................................

      • 8.2.8 Liquid Drop Model ................................

      • 8.2.9 Optical Model ....................................

      • 8.2.10 Nuclear Reactions (General).........................

      • 8.2.11 Cross-sections ....................................

      • 8.2.12 Nuclear Reactions via Compound Nucleus.............

      • 8.2.13 DirectReactions...................................

      • 8.2.14 Fission and Nuclear Reactors........................

      • 8.2.15 Fusion ...........................................



    • 8.3 Solutions.................................................. Contents xv

      • 8.3.1 AtomicMassesandRadii ...........................

      • 8.3.2 ElectricPotentialandEnergy ........................

      • 8.3.3 Nuclear Spin and Magnetic Moment ..............

      • 8.3.4 Electric Quadrupole Moment........................

      • 8.3.5 Nuclear Stability...................................

      • 8.3.6 Fermi Gas Model ................................

      • 8.3.7 Shell Model ....................................

      • 8.3.8 Liquid Drop Model ................................

      • 8.3.9 Optical Model ....................................

      • 8.3.10 Nuclear Reactions (General).........................

      • 8.3.11 Cross-sections ....................................

      • 8.3.12 Nuclear Reactions via Compound Nucleus.............

      • 8.3.13 DirectReactions...................................

      • 8.3.14 Fission and Nuclear Reactors........................

      • 8.3.15 Fusion ...........................................





  • 9 Particle Physics – I..............................................

    • 9.1 Basic Concepts and Formulae ................................

    • 9.2 Problems..................................................

      • 9.2.1 SystemofUnits ...................................

      • 9.2.2 Production ....................................

      • 9.2.3 Interaction........................................

      • 9.2.4 Decay ...........................................

        • Counters 9.2.5 Ionization Chamber, GM Counter and Proportional



      • 9.2.6 Scintillation Counter...............................

      • 9.2.7 Cerenkov Counter ................................

      • 9.2.8 SolidStateDetector................................

      • 9.2.9 Emulsions ........................................

      • 9.2.10 Motion of Charged Particles in Magnetic Field .......

      • 9.2.11 Betatron..........................................

      • 9.2.12 Cyclotron.........................................

      • 9.2.13 Synchrotron. ....................................

      • 9.2.14 Linear Accelerator ................................

      • 9.2.15 Colliders .........................................



    • 9.3 Solutions..................................................

      • 9.3.1 SystemofUnits ...................................

      • 9.3.2 Production ....................................

      • 9.3.3 Interaction........................................

      • 9.3.4 Decay ...........................................

        • Counters 9.3.5 Ionization Chamber, GM Counter and Proportional



      • 9.3.6 Scintillation Counter...............................

        • 9.3.7 Cerenkov Counter ................................ xvi Contents

        • 9.3.8 SolidStateDetector................................

        • 9.3.9 Emulsions ........................................

        • 9.3.10 Motion of Charged Particles in Magnetic Field .......

        • 9.3.11 Betatron..........................................

        • 9.3.12 Cyclotron.........................................

        • 9.3.13 Synchrotron. ....................................

        • 9.3.14 Linear Accelerator ................................

        • 9.3.15 Colliders .........................................







  • 10 Particle Physics – II.............................................

    • 10.1 Basic Concepts and Formulae ................................

    • 10.2 Problems..................................................

      • 10.2.1 ConservationLaws.................................

      • 10.2.2 StrongInteractions.................................

      • 10.2.3 Quarks...........................................

      • 10.2.4 Electromagnetic Interactions .........................

      • 10.2.5 WeakInteractions..................................

      • 10.2.6 Electro-WeakInteractions...........................

      • 10.2.7 FeynmanDiagrams ................................



    • 10.3 Solutions..................................................

      • 10.3.1 ConservationLaws.................................

      • 10.3.2 StrongInteractions.................................

      • 10.3.3 Quarks...........................................

      • 10.3.4 Electromagnetic Interactions .........................

      • 10.3.5 WeakInteractions..................................

      • 10.3.6 Electro-weakInteractions ...........................

      • 10.3.7 FeynmanDiagrams ................................



    • Appendix: Problem Index...........................................

    • Index.............................................................



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