Physics Guide

May 24th, 2024

There are many definitions of physics in standard textbooks. According to Wikipedia, “Physics is the natural science that studies the matter and its motion and behavior through space and time and that studies the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves”.

However, physics is much more than this. Physics covers the entire universe, from quantum particles to supernovas, from spinning subatomic particles to spinning galaxies. If you take physics as a subject with exams and don’t love it, you will not be able to enjoy it. Nature can be understood within physics and mathematics frames. In addition, you should know that mathematics is an essential tool in studying physics. Mathematics is the language of physics. Physics is philosophy without mathematics. Therefore, early, when scientists didn’t apply mathematics to their theories, they were called Philosophers, not physicists.

So, you want to be a successful physicist .. This page was prepared for young physicists thrilled by the challenges posed by studying physics ..

1. Skills We Need to Starting Your Physics Career

Physics is a challenging subject; it is a combination of math and science that can be difficult. Here, I will mention the main skills we need to start our physics career.

A. Language skills

English is a prerequisite. You should learn it to be able to read, write, speak and understand English. All textbooks and publications are in English. Every publication is available in English. Take note of how crucial it is to be able to write in English. You will eventually want to publish your findings. Your writing must be readable and understandable to others.

B. Mathematics

Math is considered the language of physics, you should be proficient in mathematics to be a successful physicist. Additionally, you should be good at mathematical concepts and how to apply them. If you dislike mathematics, you may want to pursue other educational options. In the next section, I mention the main mathematical topics we need to study in physics. 

C. Physics isn’t only math; it requires conceptual understanding too!

In addition to having practical knowledge of math, you should understand the physics concepts and principles. Without understanding the physics concepts and principles, the mathematical formulas and equations cannot get you so far in a physics career. Physics combines fundamental concepts and principles in addition to mathematical formulas and equations. 

D. Problem-Solving & Scientific Reasoning

In addition to mathematics, after you understand the fundamental concepts and principles, you should know how to tackle a problem and apply logical reasoning to arrive at a solution. So, you should know how to use the scientific method and the other tools physicists use, in addition to learning about related fields to physics. 

E. Physics builds on itself: Make sure you know the basics!

Physics builds on itself; it can be hard to understand upper-level physics if you don’t understand the basics.

2. Mathematical Physics

Before diving into physics and working through the concepts in the sections below, you should be proficient in mathematics to be a successful physicist. You should be good at mathematical concepts and how to apply them. Math is considered the language of physics, so if you dislike mathematics, you may want to pursue other educational options. Here, I will mention the main mathematical topics we need to study in physics: 

A. Basic mathematics 

Algebraic equations, Solving Equations and Inequalities, Graphing and Functions, Approximation techniques, Polynomial Functions, Exponential and Logarithm Functions, Systems of Equations, Series & Sequences, Trigonometry. I recommend that you study Paul Dawkins's lectures on algebra.

B. Calculus 

In a nutshell, calculus is the study of change. You will probably spend a good deal of your mathematics education studying calculus, including Limits, Differentiation, and Integration. Thomas' Calculus is one of the most favorable introductory books for studying calculus. Additionally, I recommend studying Paul Dawkins's lectures in Calculus I, Calculus II, and Calculus III.

C. Matrix and Determinant

Matrices, Laws and Properties of Matrices, Calculus in the Matrices Space, Determinants, Using Matrices in Algebra, and Eigenvalues and Eigenvectors. Here, I recommend studying Mathematical Methods for Physicists, A Comprehensive Guide by Arfken, Weber, and Harris.

D. Vectors Analysis

Vector Algebra, Curvilinear Coordinates, and Vector Calculus. Here, I recommend studying Mathematical Methods for Physicists, A Comprehensive Guide by Arfken, Weber, and Harris.

E. Differential Equations 

First and second order DEs, Series Methods, Laplace transform, Sturm-Liouville Theory, Green’s Theorem and Partial DEs. Here, I recommend studying Ordinary Differential Equations by Morris Tenenbaum and Harry Pollard, and Partial Differential Equations: An Introduction by Walter A. Strauss. You can also read Paul Dawkins lectures in Differential equations.

 F. Complex Variable Theory

Complex Algebra, Cauchy-Riemann Equations, Cauchy theorems and contour integration, Laurent Expansion, Mapping, Calculus of Residues. Here, I recommend studying Complex Analysis: A First Course with Applications by Dennis G. Zill and Patrick D. Shanahan, and Visual Complex Analysis, by Tristan Needham.

G. Integral transform

Laplace transform and Fourier Transform. Here, I recommend studying Mathematical Methods for Physicists, A Comprehensive Guide by Arfken, Weber, and Harris.

H. Special Functions 

Gamma function, Bessel Functions Legendre Functions, Hermite Functions, Laguerre Functions. Here, I recommend studying Mathematical Methods for Physicists, A Comprehensive Guide by Arfken, Weber, and Harris.

I. Vector Spaces and Eigenvalue Problems

Linear vector space, Eigenvalue Problems. Here, I recommend studying Mathematical Methods for Physicists, A Comprehensive Guide by Arfken, Weber, and Harris. In addition, you can study Introduction to Linear Algebra, Fifth Edition by Gilbert Strang.

3. Classical Mechanics

Mechanics is generally taken to mean the study of the motion of objects (or their lack of motion) under the action of given forces. Classical mechanics is sometimes considered a branch of applied mathematics. It consists of kinematics, the description of motion, and dynamics, the study of the action of forces in producing either motion or static equilibrium, these topics are important to know:

Here I recommend studying:

Also you can see Prof. David Tong lectures of Dynamics and Relativity  and Classical Dynamics 

4. Waves, Vibrations and Optics

The mechanics of vibrations and waves are complex and important enough to demand their own course of study, whereas Optics is the branch of physics that studies the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it, these topics are important to know:

Here I recommend studying The Physics of Vibrations and Waves by H. John Pain, and Optics by Eugene Hecht

5. Electromagnetism 

Electricity and Magnetism is required-- you should understand Green's functions solutions to EM problems. This is frequently not taught until graduate EM and goes well beyond Griffith's Introduction to Electrodynamics. Here Jackson's Classical Electrodynamics is the best book. These topics are important to know:

Here I recommend studying:

6. Quantum Mechanics

Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. these topics are important to know:

There are many textbooks that cover the Quantum Mechanics topic we need as a physicist, but I suggest reading:

7. Thermodynamics and Statistical Mechanics

Statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles. Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. In particular, it describes how thermal energy is converted to and from other forms of energy and how it affects matter, these topics are important to know:

There are many textbooks that cover the statistical mechanics topic we need as a physicist, such as:

8. Solid State Physics

Solid state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from their atomic-scale properties. Thus, solid-state physics forms a theoretical basis of materials science. It also has direct applications, for example in the technology of transistors and semiconductors, these topics are important to know:

I recommed  Solid-State Physics by Ashcroft and Mermin, and Introduction to Solid State Physics by Kittel. Also you can see Prof. David Tong lectures of Solid State Physics and Quantum Hall Effect 

10. Quantum Field Theory

Quantum Field Theory (QFT) is the heart of all modern high-energy physics: the Standard Model of particle physics is a QFT. The whole idea behind QFT is that we are doing quantum mechanics on classical fields, and it works remarkably well. Along with GR, QFT will be the most challenging part of your physics education, but perhaps the most rewarding (I know it was extraordinarily rewarding for me!). It may take many, many years to master. You'll learn about how to:

I recommend to studying:

11. Electives

Having mastered the principles of physics, you now possess a strong basis upon which to study more complex and specialised subjects, such as (but not restricted to): 

A. Electronics

The field of electronics is a branch of physics and electrical engineering that deals with the behavior and effects of electrons using electronic devices. You shough learn very basic things about electronic circuits also. I recommend studying Basic Electronics for Scientists and Engineers by Eggleston.

B. Special and General Relativity

I recommend studying Concepts of Modern Physics by Arthur Beiser, Spacetime and Geometry: An Introduction to General Relativity by Sean M. Carroll, and Einstein Gravity in a Nutshell by Anthony Zee.

C. Astronomy and Astrophysics

I recommend studying Cosmic Perspective by by Bennett, Donahue, Schneider, Voit and An Introduction to Modern Astrophysics by Carroll and Ostlie.

D. Biophysics

I recommend studying Biophysics: An Introduction by Glaser.

E. Particle Physics

I recommend studying Introduction to Elementary Particles by by David Griffiths (Undergraduate) and Quarks and Leptons by Halzen and Martin (Graduate).

F. Quantum Computing 

Quantum Computation and Quantum Information by Michael A. Nielsen and Isaac L. Chuang. 

G. String Theory

I recommend studying A First Course in String Theory by Zwiebach. 

H. Other

Nuclear Physics, Radiation Physics, Atomic Physics, Semiconductor physics, and Plasma physics.

Other Resources

For further reading see the following suggested links:

1) David Tong's website.

2) Gary Wysin's website.

3) How to become a good theoritical physicist - Gerard't Hooft.

4) Feynman Lectures on Physics.