Fundamentals of Physics II: Electromagnetism, Optics, and Quantum Mechanics by R. Shankar, ISBN-13: 978-0300243789

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Fundamentals of Physics II: Electromagnetism, Optics, and Quantum Mechanics by R. Shankar, ISBN-13: 978-0300243789

[PDF eBook eTextbook]

• Publisher: ‎ Yale University Press; Expanded edition (May 19, 2020)
• Language: ‎ English
• 680 pages
• ISBN-10: ‎ 0300243782
• ISBN-13: ‎ 978-0300243789

A beloved introductory physics textbook, now including exercises and an answer key, accessibly explains electromagnetism, optics, and quantum mechanics.

R. Shankar is a well‑known physicist and contagiously enthusiastic educator, whose popular online introductory-physics video lectures have been viewed over a million times. In this second book based on his online courses, Shankar explains electromagnetism, optics, and quantum mechanics, developing the basics and reinforcing the fundamentals. With the help of problem sets and answer keys, students learn about the most interesting findings of today’s research while gaining a firm foundation in the principles and methods of physics.

Table of Contents:

Preface

1. Electrostatics I

1.1. Review of F = ma

1.2. Enter electricity

1.3. Coulomb’s law

1.4. Properties of charge

1.4.1. Superposition principle

1.5. Verifying Coulomb’s law

1.6. The ratio of gravitational to electric forces

1.7. Coulomb’s law for continuous charge density

2. The Electric Field

2.1. Review of key ideas

2.2. Digression on nuclear forces

2.3. The electric field E

2.4. Visualizing the field

2.5. Field of a dipole

2.5.1. Far field of dipole: general case

2.6. Response to a field

2.6.1. Dipole in a uniform field

3. Gauss’s Law I

3.1. Field of an infinite line charge

3.2. Field of an infinite sheet of charge

3.3. Spherical charge distribution: Gauss’s law

3.4. Digression on the area vector dA

3.4.1. Composition of areas

3.4.2. An application of the area vector

3.5. Gauss’s law through pictures

3.5.1. Continuous charge density

4. Gauss’s Law II: Applications

4.1. Applications of Gauss’s law

4.2. Field inside a shell

4.3. Field of an infinite charged wire, redux

4.4. Field of an infinite plane, redux

4.5. Conductors

4.5.1. Field inside a perfect conductor is zero

4.5.2. The net charge on a conductor will reside at the surface

4.5.3. A conductor with a hole inside

4.5.4. Field on the surface of a conductor

5. The Coulomb Potential

5.1. Conservative forces and potential energy

5.2. Is the electrostatic field conservative?

5.3. Path independence through pictures

5.4. Potential and field of a dipole

6. Conductors and Capacitors

6.1. Cases where computing V from E is easier

6.2. Visualizing V

6.3. Equipotentials

6.4. Method of images

6.4.1. Proof of uniqueness (optional section)

6.4.2. Additional properties of the potential V(r)

6.5. Capacitors

6.6. Energy stored in a capacitor

6.7. Energy of a charge distribution

7. Circuits and Currents

7.1. Energy in the electric field

7.2. Circuits and conductivity

7.3. Circuits

7.4. The battery and the EMF

7.5. The RC circuit with a battery

7.6. Miscellaneous circuits

8. Magnetism I

8.1. Experiments pointing to magnetism

8.2. Examples of the Lorentz force, the cyclotron

8.3. Lorentz force on current-carrying wires

8.4. The magnetic dipole

8.5. The DC motor

9. Magnetism II: Biot-Savart Law

9.1. Practice with Biot-Savart: field of a loop

9.2. Microscopic description of a bar magnet

9.3. Magnetic field of an infinite wire

9.4. Ampère’s law

9.5. Maxwell’s equations (static case)

10. Ampère II, Faraday, and Lenz

10.1. Field of an infinite wire, redux

10.2. Field of a solenoid

10.3. Faraday and Lenz

10.4. Optional digression on Faraday’s law

11. More Faraday

11.1. Betatron

11.2. Generators

11.3. Inductance

11.4. Mutual inductance

11.5. Self-inductance

11.6. Energy in the magnetic field

12. AC Circuits

12.1. Review of inductors

12.2. The LC circuit

12.2.1. Driven LC circuit

12.3. The LCR circuit

12.3.1. Review of complex numbers

12.3.2. Solving the LCR equation

12.3.3. Visualizing Z

12.4. Complex form of Ohm’s law

13. LCR Circuits and Displacement Current

13.1. Analysis of LCR results

13.1.1. Transients and the complementary solution

13.2. Power of the complex numbers

13.3. Displacement current

14. Electromagnetic Waves

14.1. The wave equation

14.2. Restricted Maxwell equations in vacuum

14.2.1. Maxwell equations involving infinitesimal cubes

14.2.2. Maxwell equations involving infinitesimal loops

14.3. The wave!

14.4. Sinusoidal solution to the wave equation

14.5. Energy in the electromagnetic wave

14.6. Origin of electromagnetic waves

14.7. Maxwell equations—the general case (optional)

14.7.1. Maxwell equations involving infinitesimal cubes

14.7.2. Maxwell equations involving infinitesimal loops

14.7.3. Consequences for the restricted E and B

14.8. From microscopic to macroscopic (optional)

14.8.1. Maxwell equations involving cubes

14.8.2. Maxwell equations involving loops

15. Electromagnetism and Relativity

15.1. Magnetism from Coulomb’s law and relativity

15.2. Relativistic invariance of electrodynamics

15.3. Review of Lorentz transformations

15.3.1. Implications for Newtonian mechanics

15.4. Scalar and vector fields

15.5. The derivative operator

15.6. Lorentz scalars and vectors

15.7. The four-current J

15.7.1. Charge conservation and the four-current J

15.8. The four-potential A

15.8.1. Gauge invariance

15.9. Wave equation for the four-vector A

15.9.1. Why work with V and A?

15.10. The electromagnetic tensor

15.10.1. Tensors

15.10.2. The electromagnetic field tensor

16. Optics I: Geometric Optics Revisited

16.1. Geometric or ray optics

16.2. Brief history of c

16.3. Some highlights of geometric optics

16.4. The law of reflection from Fermat’s principle

16.5. Snell’s law from Fermat’s principle

16.6. Reflection off a curved surface by Fermat

16.7. Elliptical mirrors and Fermat’s principle

16.8. Parabolic mirrors

17. Optics II: More Mirrors and Lenses

17.1. Spherical approximations to parabolic mirrors

17.2. Image formation: geometric optics

17.2.1. A midlife crisis

17.3. Image formation by Fermat’s principle

17.4. Tricky cases

17.4.1. Fermat’s principle for virtual focal points

17.4.2. Ray optics for virtual images

17.5. Lenses à la Fermat

17.6. Principle of least action

17.7. The eye

18. Wave Theory of Light

18.1. Interference of waves

18.2. Adding waves using real numbers

18.3. Adding waves with complex numbers

18.4. Analysis of interference

18.5. Diffraction grating

18.6. Single-slit diffraction

18.7. Understanding reflection and crystal diffraction

18.8. Light incident on an oil slick

18.8.1. Normal incidence

18.8.2. Oblique incidence

19. Quantum Mechanics: The Main Experiment

19.1. Double-slit experiment with light

19.2. Trouble with Maxwell

19.3. Digression on photons

19.3.1. Photoelectric effect

19.3.2. Compton effect

19.4. Matter waves

19.5. Photons versus electrons

19.6. The Heisenberg uncertainty principle

19.6.1. There are no states of well-defined position and momentum

19.6.2. Heisenberg microscope

19.7. Let there be light

19.8. The wave function ψ

19.9. Collapse of the wave function

19.10. Summary

20. The Wave Function and Its Interpretation

20.1. Probability in classical and quantum mechanics

20.2. Getting to know ψ

20.3. Statistical concepts: mean and uncertainty

21. Quantization and Measurement

21.1. More on momentum states

21.2. Single-valuedness and quantization of momentum

21.2.1. Quantization

21.2.2. The integral of ψp(x)

21.3. Measurement postulate: momentum

21.3.1. An example solvable by inspection

21.3.2. Using a normalized ψ

21.4. Finding A(p) by computation

21.5. More on Fourier’s theorems

21.6. Measurement postulate: general

21.7. More than one variable

22. States of Definite Energy

22.1. Free particle on a ring

22.1.1. Analysis of energy levels: degeneracy

22.2. Thinking inside the box

22.2.1. Particle in a well

22.2.2. The box: an exact solution

22.3. Energy measurement in the box

23. Scattering and Dynamics

23.1. Quantum scattering

23.1.1. Scattering for E > V0

23.1.2. Scattering for E < V0

23.2. Tunneling

23.3. Quantum dynamics

23.3.1. A solution of the time-dependent Schrödinger equation

23.3.2. Derivation of the particular solution ψE(x, t)

23.4. Special properties of the product solution

23.5. General solution for time evolution

23.5.1. Time evolution: a more complicated example

24. Summary and Outlook

24.1. Postulates: first pass

24.2. Refining the postulates

24.2.1. Toward a compact set of postulates

24.2.2. Eigenvalue problem

24.2.3. The Dirac delta function and the operator X

24.3. Postulates: final

24.4. Many particles, bosons, and fermions

24.4.1. Identical versus indistinguishable

24.4.2. Implications for atomic structure

24.5. Energy-time uncertainty principle

24.6. What next?

Constants

Index

R. Shankar is Josiah Willard Gibbs Professor of Physics, Yale University. He is winner of the American Physical Society’s Lilienfeld Prize and author of five textbooks, including Principles of Quantum Mechanics, Basic Training in Mathematics, and Quantum Field Theory and Condensed Matter Physics.

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