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ModPhy1/

11/19/01


 

 

Contents


Page

Topic

1

Modern Physics 1

2

 Contents

3

Syllabus - Course schedule and requirements.

4

Introduction - An Internet Course in Modern Physics.

41

    Navigation through the Course        

411

        Next

42

    Structure of the Course

421

        Linear Structure

422

        Tree Structure

423

        How to Study

43

    Prerequisites for the Course

44

    Correspondence Principle

 

 

5

Unit 1. The Theory of Relativity

51

    Special Relativity

511

        Inertial Frame

5111

           Law of Inertia

51111

              Isolated Object

5112

           Frames of Reference

51121

              Coordinate System

5113

          Non-inertial Frames

51131

              Fictitious Forces

512

        Principle of Relativity

513

        Speed of Light

5131

           Double Stars

5132

           Ether

5133

           Michelson-Morley Experiment

5134

           Stellar Aberration

514

        Star Trek Paradox

515

        Relative Viewpoint

5151

           Lorentz Transform (Gamma)

51511

              Galilean Transform

5152

           Space is Relative

51521

               Length Contraction

515211

                   Pole and Barn Paradox

5153

           Time is Relative

51531

               Time Dilation

51532

               Simultaneity

515321

                   Principle of Causality

5153211

                       Time Travel

5153212

                       Superluminal Velocities

51532121

                           Tachyons

51532122

                           Proper Frame

51533

               Doppler Effect

51534

               Twin Paradox

5154

           Velocity is Relative

51541

               Galilean Velocities

51542

                Lorentz Velocities

515421

                    Headlight Effect

5155

           Mass is Relative

51551

                Massless Particles

5156

           Momentum is Relative

5157

           Energy is Relative

51571

                Binding energy

51572

                Antimatter

515721

                    Creation and Annihilation of Particles

516

        Invariant Viewpoint

5161 

            Events are Invariant

5162

            Spacetime is Invariant

51621

                Mapping versus Modeling

51622

                Spacetime Diagrams

516221

                    Coordinates

516222

                    Normalized Diagrams

516223

                    Quantitative Diagrams

5163

             Light Cones are Invariant

51631

                    Regions of Spacetime

5164

            Worldlines are Invariant

51641

                Timelines

51642

                 Spacelines

51643

                 Null-Lines

51644

                 Perpendicular Lines

5165

            Intervals are Invariant

51651 

                Metric Equation

51652

                Spacetime Geometry

516521

                    Trigonometry

51653

                Coordinate Transformations

516531

                    Rotated Cartesian Transforms

516532

                    Lorentz Transformations

5165321

                        Conventional Units

5166

            Fourvectors are Invariant

51661

                Vector Algebra

51662

                Mass, Momentum, and Energy

51663

                Conservation Laws

5167

            Tensors are Invariant

51671

               Area Tensor

51672

               Spring Constant Tensor

51673

               Matter Tensor

51674

               Electromagnetic Field Tensor

517

            Summary

52

    General Relativity

521

        The Problem with Gravity

5211

            Newtonian Gravitation

522

        Principle of Equivalence

5221

            Locally Inertial Frames

523

        Curved Spaces

5231

            Extrinsic Curvature

5232

            Intrinsic Curvature

524

        Einsteinian Gravitation

5241

            Tensors

5242

            Einstein Tensor

5243

            Matter Tensor

525

        Tests of General Relativity

5251

            Orbit of Mercury

5252

            Deflection of Light

5253

            Gravitational Redshift

5254

            Gravitational Radiation

5255

            Black Holes

5256

            Cosmological Constant

5257

            Modified Field Equation

 

 

6

Unit 2. Particle-Wave Duality

61

Distribution of Matter

62

Quantization

621

    Oil Drop Experiment

622

    e/m Experiment

623

    Law of Electrolysis

63

Waves with Particle-like Properties

631

    Maxwell’s Theory

632

    Hertz’s Experiments

633

    Blackbody Radiation

6331

        Kirchhoff’s Theorem

6332

        Stefan’s Law

6333

        Wien’s Law

6334

        Rayleigh-Jeans Law

63341

            Number of Modes for Waves in a Cavity

6335

        Plank’s Law

634

    Photoelectric Effect

635

    X-Rays Scattering

6351

        Bragg Scattering

6352

        Compton Scattering

636

    Gravitational Redshift

637

    Review Problems

64

Models of the Atom

641

    Thompson’s Plumb Pudding Model

642

    Rutherford’s Nuclear Model

643

    Bohr’s Model of the Hydrogen Atom

6431

        Reduced Mass Correction

6432

        Bohr’s Correspondence Principle

644

    Frank-Hertz Experiment

645

    Review Problems

65

Particles with Wavelike Properties

651

    De Broglie Wavelength

652

    Davidsson-Germer Experiment

66

Particle-Wave Duality

661

    Particles and Waves

6611

        Particles

6612

        Waves

662

    Fourier Transformations

6621

        Fourier Transforms

6622

        Summary

663

    Wave Packets

664

    Uncertainty Principle

6641

        Classical Uncertainty

6642

        Heisenberg Uncertainty

665

    Electron Diffraction through a Double Slit

666

    Review Problems

 

 

7

Unit 3. One-Dimensional Quantum Mechanics

71

Quantum Concepts

711

    Scientific Knowledge

7111

        Quantum System

7112

        Quantum States

7113

        State Function

71131

            Polarized Light

71132

            Polarized Photons

7114

        Known Quantities

712

    Experiments

7121

        Operations

7122

        Variables

71221

            Prepared Variables

71222

            Hidden Variables

71223

            Pseudo Variables

71224

            Observables

71225

            Classifying Variables

7123

        Measurements

7124

        Detector

713

    Observables

7131

        Eigenvalues

7132

        Eigenstates

7133

        Eigenvalue Equation

7134

        Functional Relationship

7135

        Uncertainty Relationship

714

    Multiple Measurements

7141

        Superposition

7142

        Probability

7143

        Expectation Value

7144

        Uncertainty

715

    Bra-Ket Product

72

Born Interpretation

73

Fundamental Principles of Quantum Mechanics

731

    Inner Product

7311

            Normalization

7312

            Orthogonality

7313

            Complete Orthonormal Set

732

    Free Particle Wave Function

733

    Operators

7331

        Changing States

7332

        Operator Algebra

73321

            Sum

73322

            Product

733221

                Commutator

73323

            Functions of Operators

734

    Schrödinger’s Equation

735

    Observables

736

    Expectation Values

737

    Uncertainties

7371

        Sharp Observables

7372

        Uncertainty Principle

738

    Correspondence Principle

7381

            Classical Equations

7382

            T+U = E

74

One-Dimensional Applications of Quantum Mechanics

741

    Particle in a Box

742

    Particle in a Square Well

743

    Quantum Oscillator

744

    Square Barrier

745

    Field Emission

746

    Alpha Decay

747

    Ammonia Inversion

748

    Scanning Tunneling Microscope

75

Review Problems

 

 

8

Unit 4. Three-Dimensional Quantum Mechanics

81

3-D Schrodinger Equation

811

    3-D Operators

82

Particle in a 3-D Box

83

Central Forces

831

    Quantization of Angular Momentum

8311

        Magnetic Quantum Number

8312

        Orbital Quantum Number

832

    Quantization of Energy

8321

        Principle Quantum Number

84

Hydrogen Atom

841

    Radial Wave Equation

842

    Ground State

843

    Excited States

85

Orbital Magnetism

851

    Zeeman Effect

86

Electron Spin

861

    Total Angular Momentum

8611

        Spin-Orbit Coupling

87

Exchange Symmetry

871

    Exclusion Principle

88

Multi-Electron A