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Fall 2025: Physics 313 – Modern Physics

Course information

  • Title: 01:750:313 Modern Physics, Fall 2025
  • Course description: This one semester course introduces modern physics, tracing the early twentieth century revolutions that revealed how nature behaves at length and velocity scales far from everyday experience. After a brief review of classical physics (Newtonian mechanics, thermodynamics and electrodynamics) and the puzzles it could not explain, the course covers the two pillars of modern physics. The first is special relativity: Einstein’s postulates, Lorentz transformations, time dilation, length contraction and the equivalence of mass and energy. The second is quantum mechanics, developed through its experimental foundations (blackbody radiation and Planck’s hypothesis, the photoelectric effect, Compton scattering, atomic spectra, and the Rutherford and Bohr models) and through wave-particle duality (de Broglie waves, the Davisson-Germer experiment and the double-slit experiment). The course concludes with a rigorous introduction to quantum mechanics: the Schrödinger equation, wavefunctions and the Born rule, the uncertainty principle, exactly solvable systems (the particle in a box, the harmonic oscillator and quantum tunneling), and the quantum mechanical treatment of the hydrogen atom, including the Zeeman effect and electron spin. Concepts are connected throughout to real world applications such as LIGO, GPS and atomic clocks.
  • Course instructor: Srivatsan Chakram (Vatsan), schakram@physics.rutgers.edu
  • Prerequisites:
    • Mechanics and electromagnetism, either through the Analytical Physics sequence (01:750:202, 01:750:204 or 01:750:228) or the Honors Physics sequence (01:750:271 and 01:750:272)
    • Calculus (01:640:136 or 01:640:152)
  • Corequisites: None
  • Textbook: Modern Physics for Scientists and Engineers, Stephen T. Thornton, Andrew Rex and Carol Hood.
  • Class times: Two 80 minute lectures per week, on Tuesdays and Fridays
  • Location: Lucy Stone Hall (LSH) 269, Livingston Campus

Lecture schedule

Handwritten lecture notes are linked below. The complete set of slides is available here, and all of the notes live in this folder.

# Date Topics Reading Homework Notes
Module 1: Review of nineteenth century physics
1 Sep 2 Course introduction and logistics. Overview and triumphs of nineteenth century physics. Newtonian mechanics and Newton’s laws of motion. Newtonian principle of relativity. Ch 1.1 Lec 1
2 Sep 5 Math primer: complex numbers and solving differential equations. Conservation laws: energy, momentum and angular momentum. Ch 1.2–1.3 HW 1 out Lec 2
3 Sep 9 Recap of thermodynamics: the laws of thermodynamics, the second law and entropy. Kinetic theory of gases and the Maxwell-Boltzmann distribution. Electrodynamics and Maxwell’s equations. Ch 1.4–1.6 Lec 3
4 Sep 12 Electromagnetic waves and the relation between E and B fields. Energy of EM waves and the Poynting vector. Wave phenomena: interference and diffraction. The wave-particle debate and the unresolved questions of nineteenth century physics. Blackbody radiation (introduction). Ch 1.2, 1.3, 1.6 HW 2 out, HW 1 due Lec 4
5 Sep 16 Interference and diffraction continued; double-slit fringes. Searching for the ether: the Michelson-Morley experiment. Interferometry: from Michelson to LIGO. Ch 1.6, 1.7, 2.1, 2.2 Lec 5
Module 2: Special relativity
6 Sep 19 Einstein’s postulates of special relativity. Synchronization of clocks and simultaneity. Lorentz transformations. Time dilation. Ch 2.3–2.5 HW 3 out, HW 2 due Lec 6
7 Sep 23 Length contraction. Relativistic velocity addition and the Fizeau experiment. The twin paradox. Spacetime and the spacetime interval. The Doppler effect for light. Tests of special relativity. Ch 2.6–2.10 Lec 7
8 Sep 26 Relativistic momentum. Relativistic energy and the equivalence of mass and energy. The energy-momentum relation. Deriving relativistic dynamics from symmetry: translations, rotations and Lorentz transformations. Ch 2.11–2.12 HW 4 out, HW 3 due Lec 8
9 Sep 30 Experimental tests of special relativity: muon decay, atomic clocks and computations in high energy physics. Electromagnetism and relativity, invariance of charge, and the conversion between electric and magnetic fields. Ch 2.13–2.14
10 Oct 3 Introduction to general relativity and the equivalence principle. Light bent by gravity; gravity as curvature of spacetime; spacetime curved by mass. Stellar aberration and the Eddington experiment. Gravitational redshift. Gravitational waves and LIGO. HW 4 due
Oct 7 Midterm 1 (covers Ch 1–2)
Module 3: Experimental basis for quantum physics
11 Oct 10 X-rays: discovery and properties. Cathode rays and the discovery of the electron. Measuring e/m (J. J. Thomson) and e (the Millikan oil-drop experiment). Atomic spectra, the hydrogen spectrum and the Rydberg formula. Discovery of helium. Ch 3.1–3.3 HW 5 out Lec 11
12 Oct 17 Blackbody radiation: Wien’s law, the Stefan-Boltzmann law, the Rayleigh-Jeans formula and the ultraviolet catastrophe. Planck’s radiation formula and quantization. The photoelectric effect: experimental phenomenology and Einstein’s explanation. Ch 3.4–3.6 HW 5 due Lec 12
13 Oct 21 X-ray production. The Compton effect: elastic scattering of photons and electrons, and the Compton wavelength. Pair production and pair annihilation. Ch 3.7–3.9 HW 6 out Lec 13
Module 4: Structure of the atom
14 Oct 24 Brief recap of atomic history. The atomic models of Thomson and Rutherford. Alpha particles and their nature. Rutherford’s gold foil experiment. Scattering from the Coulomb interaction and the Rutherford scattering formula. Ch 4.1–4.4 Lec 14
15 Oct 28 Instability of the classical planetary atom. The Bohr model: assumptions, angular momentum quantization, deriving the Rydberg formula, and the fine structure constant. The correspondence principle. Limitations of the Bohr model. Ch 4.4–4.7 HW 7 out, HW 6 due Lec 15
16 Oct 31 The correspondence principle continued; isotope shifts and reduced mass corrections. Further limitations of the Bohr model. Wave-particle duality of matter and the de Broglie hypothesis. Deriving Bohr’s angular momentum quantization from de Broglie waves. Ch 4.5–4.7, 5.1–5.2 Lec 16
17 Nov 4 Recap of the wave equation and electromagnetic waves. Solving the wave equation: pulse-like solutions and wave packets. Fourier series and Fourier transforms. Group velocity and phase velocity. De Broglie’s derivation of the velocity of relativistic matter waves. Ch 5.2–5.5 HW 7 due Lec 17
18 Nov 7 X-ray diffraction by crystals and Bragg scattering. Proving the wave nature of matter: electron diffraction and the Davisson-Germer experiment. Waves and particles: the double-slit experiment with light and with electrons. The gedanken “which slit” experiment and how measurement changes the outcome. The principle of complementarity. Ch 5.1, 5.3, 5.5 Lec 18
Nov 11 Midterm 2 (covers Ch 3–5)
Module 5: Quantum mechanics
19 Nov 14 Gaussian wave packets in real and Fourier space. The wavefunction and the Born rule for probabilities. The Copenhagen interpretation. The uncertainty principle and the Heisenberg microscope. Δx and Δp of wave packets. Particle in a well or box (introduction). The hydrogen atom (introduction). Ch 5.5–5.8 Lec 19
20–21 Nov 18 and 21 Overview of wave mechanics and matrix mechanics. The Schrödinger equation and its consistency with Planck and de Broglie. Linearity of quantum mechanics. Quantum measurement: observables as operators. Eigenfunctions and eigenvalues; state collapse during measurement. Expectation values. The particle in an infinite square well. Ch 6.1–6.3 Lec 21 and 22
22 Dec 2 Recap of the postulates of quantum mechanics. Non-commutativity of the position and momentum operators. The infinite square well in three dimensions. The finite square well. The simple harmonic oscillator. Quantum tunneling. Ch 6.4–6.6 Lec 21 and 22, Lec 22
23 Dec 5 The Schrödinger equation for the hydrogen atom: separation of variables and quantum numbers. The atom in a magnetic field and the Zeeman effect. The magnetic moment of the electron. Electron spin and the Stern-Gerlach experiment. Relativistic corrections. Ch 7.1, 7.3–7.5 Lec 23
Final exam (cumulative)