What Does a Theoretical Physicist Do?

Corresponding to physics is divided into theoretical physics and experimental physics, physicists can also be divided into theoretical physicists and experimental physicists. Of course, theory and experiments are indispensable components in physics, so sometimes such classifications are difficult to define. It is just that in the case where a physicist is more theoretical, he or she is called a theoretical physicist, such as Einstein; if he is more experimental, he is called an experimental physicist, such as Faraday.

Theoretical physicist

Theoretical physics is like a

. Are you familiar with numbers? Addition, subtraction, multiplication, division, square root, etc.?

Many online courses on math can be found here! (More than you need)

Natural numbers: 1, 2, 3, ...

Integer: ..., -2, -1, 0, 1, 2, ...

fraction:

Real numbers: Sqrt (2) = 1.4142135 ..., pi = 3.14159265 ..., e = 2.7182818 ..., ...

Complex numbers: 2 + 3i, eia = cos a + i sin a, ... they are very important!

Set theory: open set, compact space, topology.

You may find it strange that they are indeed useful in physics.

Dave E. Joyce's Trigonometric Functions Course

This is a must: plural classes taught by James Binney

(Almost) all of the above, here! (K. Kubota, Kentucky). See also Chris Pope's handout: Methods1-ch1 Methods1-ch2

Complex plane. Cauchy's theorem and Wai integral (G. Cain, Atlanta)

Algebraic equation. Approximate method. Series expansion: Talylor series. Solve complex equations. Trigonometric functions: sin (2x) = 2sin x cos x, etc.

Infinitely small. differential. Differentiate the basic functions (sin, cos, exp).

Integral, if possible, find the integral of the basic function.

Differential equations. System of linear equations

Fourier transform. Use of plural. Convergence of series.

Complex plane. Cauchy's theorem and the Wai integral method (this is interesting now).

Gamma function (enjoy the fun while learning his nature).

Gaussian points. Probability theory.

Partial differential equations. Dirichlet and Neumann boundary conditions.

These are for beginners. Some content may serve as a complete lecture course. Most of these contents are necessary in physics theory. You don't need to complete all of these lessons when you start learning the latter, but remember to come back later to complete the ones you missed the first time.

A set of very good handouts from Harvard;

More explanations of Lagrange and Hamilton equations

AA Louro's Optical Lecture

Alfred Huan's "Statistical Mechanics" Textbook

Thermodynamics Lecture by Professor Donald B. Melrose

Classical mechanics: statics (force, stress); hydrostatics. Newton's law.

Planet's elliptical orbit. Multibody problems.

Action principle. Hamilton equation. Lagrange (don't skip it, it's important!)

Resonator. put.

Poisson brackets.

Wave equation. Liquids and gases. Viscosity. Navier-Stokes equation. Viscosity and friction.

Optics: Refraction and reflection. Lenses and mirrors. Telescope and microscope. Introduction to wave propagation. Doppler effect. The Huygens' principle of superposition of waves. Wavefront. Caustics.

Statistical Mechanics and Thermodynamics: First, Second, and Third Laws of Thermodynamics.

Boltzmann distribution.

Kano cycle. entropy. hot.

Phase change. Thermodynamic model.

Ising model (deferring the technique of solving the 2-dimensional Ising model to the back).

Planck's Law of Radiation (as a prelude to quantum mechanics)

(Just some very basic) electronics: circuits. Ohm's Law. Capacitance, inductance, use complex numbers to calculate their effects. Transistors, diodes (they work later).

Mathematica for Students of Science by James Kelly Angus MacKinnon, Computational Physics

W. .J. Spence, Electromagnetism

Bo Thide EM Field theory text (advanced)

Exercises already done in Jackson's book, set 1 / set 2

Introduction to QM and special relativity: Michael Fowler

An alternative Introduction

Niels Walet lecture course on QM (Manchester) lecture notes

Even the purest theorists may be interested in certain aspects of computational physics.

Maxwell's theory of electromagnetics. Maxwell's law (uniform and non-uniform)

Maxwell's law in the medium. boundary. Solve the equations in these cases:

Vacuum and homogeneous media (electromagnetic waves);

In a box (waveguide);

On the boundary (refraction and reflection);

(Non-relativity) Quantum mechanics. Bohr atom

De Broglie relationship (energy-frequency, momentum-wave number)

Schrödinger equation (with potential and magnetic field)

Allen Fries theorem

A particle in the box

The hydrogen atom gives a detailed solution process. Zeeman effect. Stark effect.

Quantum harmonic oscillator.

Operators: energy, momentum, angular momentum, generation and destruction operators.

Reciprocal relationship between them.

An introduction to scattering theory in quantum mechanics. S matrix. Radioactive decay.

Atoms and molecules. Chemical bonding. track. Atomic and molecular spectrum. Emission and absorption of light. Quantum Selection Rule. Magnetic moment.

Solid State Physics: notes by Chetan Nayak (UCLA)

Solid physics. Crystals. Prague reflection. Crystal group. Dielectric constant and diamagnetic permeability. Bloch spectrum. Fermi level. Conductors, semiconductors and insulators. Specific heat. Electrons and holes. Transistor. Superconducting. Hall Effect.

Nuclear physics. isotope. radioactivity. Fission and fusion. Droplet model. The quantum number of the nucleus. Magic number core. Isospin. Yukawa Theory.

Plasma Physics: Magnetohydrodynamics, Alvin Wave.

See John Heinbockel, Virgunia.

See Chr. Pope: Methods2

G.'t Hooft: Lie groups, in Dutch + exercises

Special functions and polynomials (you don't need to remember these, just understand it).

Advanced Mathematics: Group Theory, and Linear Representation of Groups. Lie group theory. Vector and tensor.

More techniques for solving (partial) differential and integral equations.

Extreme value principle and approximation techniques based on it.

Difference equation. Generate function. Hilbert space.

Introduction to Functional Integrals.

Peter Dunsby's lecture course on tensors and special relativity

Michigan notes on (advanced) Quantum Mechanics

Special theory of relativity. Lorentz transformation. Lorentz shrinks and time expands. E = mc2. 4-vector and 4-tensor. Transformation rules for Maxwell's equations. Relativity Doppler Effect.

Advanced Quantum Mechanics: Hilbert Space. Atomic transition. Emission and absorption of light. Stimulated emission. Density matrix. An explanation of quantum mechanics. Bell's inequality. Transition to Relativistic Quantum Mechanics: Dirac Equation, Fine Structure. Electron and positron. BCS theory of superconductivity. Quantum Hall effect. Advanced scattering theory. Dispersion relationship. The perturbation unfolds. WKB is approximate. Extreme value principle. Bose-Einstein condensation. Superfluid liquid helium.

More phenomenological theories: subatomic particles (mesons, baryons, photons, leptons, quarks) and cosmic rays; material properties and chemistry; nuclear isotopes; phase transitions; astrophysics (planets, stars, galaxies, redshifts) , Supernova); cosmology (cosmological model, skyrocketing universe theory, microwave background radiation); detection technology.

Introduction + exercises by G. 't Hooft

Alternative: Sean M. Carrol's lecture notes on GR

Pierre van Baal's notes on QFT

General relativity. Metric tensor. Spatiotemporal curvature. Einstein's gravitational equation. Schwarzchard black hole; Lisnell-Roztaum black hole The perihelion moves. Gravitational lens. Model of the universe. Gravitational radiation.

Quantum field theory. Classical fields: scalar field, Dirac-spin field, Young-Mills vector field.

Interaction, perturbation unfolds. Spontaneous symmetry breaks, Goldstone's mode. Higgs mechanism.

Particles and fields: Fokker space. Antiparticle. Feynman rules. Meson and nuclear De Gelman-Levi Sigma model. Circle illustration. What is positive, causal and dispersion. Renormalization (Bouli-Vilas; dimensional renormalization). Quantum gauge theory: gauge fixation, Fatiev-Popov determinant, Slavov identity, BRST symmetry. Renormalize the swarm. Progressive freedom.

Solitons, Skyrmions. Magnetic monopoles and instantons. Quark confinement mechanism. 1 / N expansion. Operator product expansion. Beta-Sapetta equation. The standard model is established. P and CP are destroyed. CPT theorem. The link between spin and statistics. Super symmetric.

Introduction + exercises

A more general site for superstrings

Superstring theory.

More online handouts can be found here.

Books. There are many books on various topics in theoretical physics.

Few books are listed here:

H. Margenau and GM Murphy, The Mathematics of Physics and Chemistry, D. v. Nostrand Comp.

R. Baker, Linear Algebra, Rinton Press

LE Reichl: A Modern Course in Statistical Physics, 2nd ed.

RK Pathria: Statistical Mechanics

M. Plischke & B. Bergesen: Equilibrium Statistical Physics

LD Landau & EM Lifxxxxz: Statistical Physics, Part 1

S.-K. Ma, Statistical Mechanics, World Scientific

JD Jackson, Classical Electrodynamics, 3rd ed., Wiley & Sons.

A. Das & AC Melissinos, Quantum mechanics, Gordon & Breach

AS Davydov, Quantum Mechanics. Pergamon Press

E. Merzbacher, Quantum Mechanics, Wiley & Sons

R. Shankar, Principles of Quantum Mechanics, Plenum

JJ Sakurai, Advanced Quantum Mechanics, Addison-Wesley

B. de Wit & J. Smith, Field Theory in Particle Physics, North-Holland

IJR Aitchison & AJG Hey, Gauge Theories in Particles Physics, Adam Hilger

LH Ryder, Quantum Field Theory, Cambridge Univ. Press

C. Itzykson & J.-B. Zuber, Quantum Field Theory, McGraw-Hill.

MB Green, JH Schwarz & E. Witten, Superstring theory, Vols. I & II, Cambridge Univ. Press

J. Polchinski, String Theory, Vols. I & II, Cambridge Univ. Press

Other useful textbook books can be found here: Mathematics, Physics (many here are for pastime, not understanding the basics of the world)

There have been some responses. I thank: Rob van Linden, Robert Tough, Thuy Nguyen, Tina Witham, Jerry Blair, Jonathan Martin and others.

Last revised: February 20, 2003