Physics Roadmap - Zero to Research Level

🔬 Complete Physics Roadmap

From Zero to Research Level

Stage 1: Mathematical & Scientific Foundation

Duration: 6-12 months

1.1 Basic Mathematics

Algebra: Linear equations, quadratic equations, polynomials, inequalities
Geometry: Euclidean geometry, coordinate geometry, trigonometry
Pre-Calculus: Functions, graphs, limits introduction
Basic Statistics: Mean, median, mode, standard deviation

1.2 Calculus Fundamentals

Differential Calculus: Derivatives, chain rule, product rule, applications
Integral Calculus: Indefinite integrals, definite integrals, techniques
Multivariable Calculus: Partial derivatives, multiple integrals, gradient
Vector Calculus: Divergence, curl, line integrals, surface integrals

1.3 Linear Algebra

Vectors & Matrices: Operations, transformations, determinants
Eigenvalues & Eigenvectors: Diagonalization, applications
Vector Spaces: Basis, dimension, linear independence
Inner Product Spaces: Orthogonality, Gram-Schmidt process

1.4 Scientific Method & Laboratory Skills

Scientific Method: Hypothesis, experimentation, analysis, conclusion
Measurement & Units: SI units, dimensional analysis, significant figures
Error Analysis: Systematic errors, random errors, uncertainty propagation
Data Visualization: Graphs, charts, scientific reporting

Stage 2: Classical Physics

Duration: 12-18 months

2.1 Classical Mechanics

Kinematics: Motion in 1D, 2D, 3D; projectile motion; relative motion
Newton's Laws: Force, mass, acceleration; friction; circular motion
Work & Energy: Kinetic energy, potential energy, conservation laws
Momentum: Linear momentum, collisions, center of mass
Rotational Mechanics: Torque, angular momentum, moment of inertia
Oscillations: Simple harmonic motion, damped oscillations, forced oscillations
Gravitation: Newton's law of gravitation, orbital mechanics, Kepler's laws

2.2 Waves & Acoustics

Wave Properties: Wavelength, frequency, amplitude, wave speed
Wave Types: Transverse, longitudinal, standing waves
Sound Waves: Properties, Doppler effect, interference
Superposition: Beats, resonance, harmonics

2.3 Thermodynamics

Temperature & Heat: Thermal equilibrium, heat transfer mechanisms
First Law: Internal energy, work, heat; enthalpy
Second Law: Entropy, heat engines, refrigerators; Carnot cycle
Third Law: Absolute zero, entropy at low temperatures
Kinetic Theory: Ideal gas law, Maxwell-Boltzmann distribution

2.4 Electromagnetism

Electrostatics: Coulomb's law, electric field, Gauss's law, potential
Capacitance: Capacitors, dielectrics, energy storage
Current Electricity: Ohm's law, circuits, Kirchhoff's laws
Magnetostatics: Magnetic field, Biot-Savart law, Ampere's law
Electromagnetic Induction: Faraday's law, Lenz's law, inductance
Maxwell's Equations: Complete formulation, electromagnetic waves

2.5 Optics

Geometric Optics: Reflection, refraction, mirrors, lenses
Wave Optics: Interference, diffraction, polarization
Optical Instruments: Microscopes, telescopes, spectrometers
Modern Optics: Lasers, fiber optics, holography basics

Stage 3: Modern Physics

Duration: 12-18 months

3.1 Special Relativity

Postulates: Constancy of light speed, relativity principle
Time Dilation: Proper time, Lorentz factor, twin paradox
Length Contraction: Proper length, relativistic effects
Relativistic Momentum & Energy: Mass-energy equivalence (E=mc²)
Four-Vectors: Spacetime, Minkowski diagrams, Lorentz transformations

3.2 Quantum Mechanics Foundations

Wave-Particle Duality: Photoelectric effect, Compton effect, de Broglie waves
Atomic Models: Bohr model, hydrogen spectrum, atomic orbitals
Schrödinger Equation: Time-dependent and time-independent forms
Quantum States: Wave functions, probability density, normalization
Uncertainty Principle: Heisenberg's principle, complementarity
Quantum Numbers: Principal, angular, magnetic, spin

3.3 Atomic & Molecular Physics

Atomic Structure: Multi-electron atoms, Pauli exclusion principle
Spectroscopy: Emission, absorption, selection rules
Molecular Bonding: Covalent, ionic, metallic bonds
Molecular Spectroscopy: Rotational, vibrational, electronic spectra

3.4 Nuclear Physics

Nuclear Structure: Protons, neutrons, binding energy, nuclear forces
Radioactivity: Alpha, beta, gamma decay; half-life; decay chains
Nuclear Reactions: Fission, fusion, reaction cross-sections
Applications: Nuclear power, medical applications, dating methods

3.5 Statistical Mechanics

Ensemble Theory: Microcanonical, canonical, grand canonical
Partition Functions: Single particle, multi-particle systems
Quantum Statistics: Fermi-Dirac, Bose-Einstein distributions
Applications: Blackbody radiation, specific heat, phase transitions

Stage 4: Advanced Physics

Duration: 18-24 months

4.1 Analytical Mechanics

Lagrangian Mechanics: Generalized coordinates, Euler-Lagrange equations
Hamiltonian Mechanics: Phase space, Hamilton's equations, Poisson brackets
Canonical Transformations: Generating functions, action-angle variables
Hamilton-Jacobi Theory: Complete integrals, separation of variables
Chaos & Nonlinear Dynamics: Lyapunov exponents, strange attractors

4.2 Advanced Electromagnetism

Electromagnetic Potentials: Scalar & vector potentials, gauge transformations
Radiation: Dipole radiation, antenna theory, synchrotron radiation
Relativistic Electrodynamics: Covariant formulation, field tensors
Electromagnetic Waves in Media: Dispersion, absorption, metamaterials

4.3 Advanced Quantum Mechanics

Dirac Notation: Bra-ket formalism, Hilbert spaces
Angular Momentum: Ladder operators, addition of angular momenta, Clebsch-Gordan
Perturbation Theory: Time-independent, time-dependent, degenerate cases
Scattering Theory: Partial waves, Born approximation, cross-sections
Identical Particles: Symmetrization, antisymmetrization, second quantization

4.4 General Relativity

Differential Geometry: Manifolds, tensors, metric, covariant derivative
Einstein Field Equations: Stress-energy tensor, curvature
Solutions: Schwarzschild, Kerr, FLRW metrics
Black Holes: Event horizons, singularities, Hawking radiation
Gravitational Waves: Production, detection, LIGO/Virgo discoveries

4.5 Solid State Physics

Crystal Structure: Bravais lattices, reciprocal lattice, Brillouin zones
Lattice Dynamics: Phonons, thermal properties, Debye model
Electronic Properties: Band theory, metals, insulators, semiconductors
Magnetic Properties: Diamagnetism, paramagnetism, ferromagnetism
Superconductivity: BCS theory, Cooper pairs, Meissner effect

Stage 5: Specialization Tracks

Duration: 24-36 months

5.1 Particle Physics & High Energy Physics

Standard Model: Quarks, leptons, gauge bosons, Higgs mechanism
Quantum Field Theory: Canonical quantization, Feynman diagrams
Quantum Electrodynamics: QED calculations, renormalization
Quantum Chromodynamics: Color charge, asymptotic freedom, confinement
Electroweak Theory: Unification, symmetry breaking, neutrino physics
Beyond Standard Model: Supersymmetry, grand unification, string theory

5.2 Astrophysics & Cosmology

Stellar Astrophysics: Stellar structure, evolution, nucleosynthesis
Compact Objects: White dwarfs, neutron stars, black holes
Galactic Astrophysics: Galaxy formation, dynamics, dark matter
Cosmology: Big Bang, inflation, cosmic microwave background
Dark Energy: Accelerating universe, cosmological constant
Multi-messenger Astronomy: Gravitational waves, neutrinos, high-energy particles

5.3 Condensed Matter Physics

Many-Body Theory: Green's functions, Feynman diagrams for condensed matter
Topological Matter: Topological insulators, Weyl semimetals
Quantum Materials: High-Tc superconductors, heavy fermions
Low-Dimensional Systems: Graphene, 2D materials, quantum wells
Soft Matter: Polymers, colloids, liquid crystals
Spintronics: Spin transport, magnetic nanostructures

5.4 Quantum Information & Computing

Quantum Bits: Superposition, entanglement, measurement
Quantum Gates: Universal gate sets, circuit model
Quantum Algorithms: Shor's, Grover's, variational algorithms
Quantum Error Correction: Stabilizer codes, fault tolerance
Physical Implementations: Superconducting qubits, ion traps, photonics
Quantum Communication: Quantum cryptography, teleportation

5.5 Atomic, Molecular & Optical Physics

Laser Physics: Stimulated emission, laser types, ultrafast lasers
Atom Trapping & Cooling: Laser cooling, magneto-optical traps, BEC
Precision Measurements: Atomic clocks, spectroscopy, metrology
Quantum Optics: Photon statistics, squeezed states, cavity QED
Ultrafast Physics: Femtosecond dynamics, attosecond science

5.6 Nuclear & Plasma Physics

Nuclear Structure: Shell model, collective models, exotic nuclei
Heavy Ion Physics: Quark-gluon plasma, RHIC, LHC experiments
Plasma Physics: MHD, kinetic theory, waves in plasmas
Fusion Energy: Tokamaks, inertial confinement, ITER
Space Plasma: Solar wind, magnetospheric physics

Stage 6: Research Level Physics

Duration: 4-6+ years (PhD)

6.1 Research Skills Development

Literature Review: Reading papers, identifying gaps, research questions
Research Methodology: Experimental design, computational methods
Scientific Writing: Papers, grants, thesis writing
Presentation Skills: Conferences, seminars, poster presentations
Collaboration: Working with research groups, international collaborations

6.2 Computational Physics

Numerical Methods: ODEs, PDEs, Monte Carlo methods
Simulation Techniques: Molecular dynamics, lattice QCD, DFT
Machine Learning in Physics: Neural networks, data analysis, discovery
High-Performance Computing: Parallel computing, GPU programming

6.3 Experimental Techniques

Detector Physics: Particle detectors, radiation detection
Instrumentation: Electronics, data acquisition systems
Vacuum Technology: UHV systems, cryogenics
Advanced Spectroscopy: X-ray, neutron scattering techniques

6.4 Frontier Research Areas

Quantum Gravity: Loop quantum gravity, string theory, holography
Dark Matter Detection: Direct detection, indirect searches
Quantum Simulation: Cold atoms, trapped ions, analog quantum computers
Precision Tests: Tests of fundamental symmetries, new physics searches
Emergent Phenomena: Complexity, self-organization, far-from-equilibrium systems

6.5 Professional Development

Teaching: Undergraduate instruction, mentoring
Grant Writing: Funding proposals, budgeting
Peer Review: Reviewing papers, serving on committees
Science Communication: Public outreach, media engagement
Career Paths: Academia, industry, national labs, policy

📊 Physics Learning Flowchart

START

Mathematics Foundation Algebra, Calculus, Linear Algebra

Math Ready?

Classical Physics Mechanics, Waves, Thermo, EM

Modern Physics Relativity, QM, Nuclear, Statistical

Core Complete?

Advanced Topics Analytical Mech, GR, QFT basics

Particle Physics

Astrophysics

Condensed Matter

Quantum Info

Research Level PhD Research, Publications, Expertise

PHYSICIST

🧠 Physics Mind Map

🛤️ Visual Learning Roadmap

🚀 Start

Begin your physics journey

Day 1

📐 Mathematics

Calculus, Linear Algebra, Vector Calculus

6-12 months

⚙️ Classical Physics

Mechanics, Waves, Thermo, EM, Optics

12-18 months

⚛️ Modern Physics

Relativity, Quantum Mechanics, Nuclear

12-18 months

🔬 Advanced Topics

Analytical Mech, GR, Advanced QM

18-24 months

🎯 Specialization

Choose: Particle, Astro, Condensed, Quantum

24-36 months

🔭 Research Level

PhD Research, Publications, Expertise

4-6+ years

🏆 Physicist

Contributing to human knowledge

Lifetime

⚠️ Educational Disclaimer

This resource is for educational purposes only and does not constitute legal advice.

The information provided in this roadmap is intended as a general guide for learning physics. Individual learning paths may vary based on personal goals, prior knowledge, and available resources. Always consult with academic advisors, professors, or career counselors for personalized guidance.