Syllabus

Lecture 1  Dawn of New Age I (Harris Chapter 1) (8/24/2026)

The goal of this course is to become familiar with non-classical physics, learn some of the new mathematics needed to describe it, appreciate how surprising many modern-physics discoveries were, and understand how scientific knowledge evolves when an established framework encounters limits. We will begin with a historical example from mechanics and astronomy: Kepler summarized planetary motion empirically, Newton explained it dynamically, the anomaly in Mercury’s orbit exposed a limit of Newtonian gravity, and general relativity provided a broader framework. We will then follow a similar progression in electricity and magnetism, where separate electric and magnetic phenomena were unified, light was identified as an electromagnetic wave, and tensions between electromagnetism and classical mechanics ultimately helped lead to special relativity.
(Extra Recommended Reading Assignment: Read Thomas Kuhn's The Structure of Scientific Revolutions Chapter 1: Role of History)

Lecture 2  Dawn of New Age II (Harris Chapter 1) (8/26/2026)

In Lecture 2, we conclude our discussion of electromagnetism by showing how the electromagnetic wave equation emerges from Maxwell’s equations. We then explore how the constant speed of light, motivated Einstein’s formulation of special relativity. Finally, we examine the failure of classical equipartition to describe heat capacity, where predictions of a constant value break down at low temperatures. This anomaly was resolved by Einstein and Debye, whose quantum vibrational models accurately capture the drop to zero and mark an early milestone of quantum theory. 

(Review Maxwell's equations, Specific heat of diamond )

Lecture 3  Hollistic view of Modern Physics (Harris Chapter 1) (8/31/2026)

In lecture 3, I will provide a holistic overview of modern physics, detailing the evolution from classical mechanics to quantum mechanics and special relativity. We will also explore how to think about high-energy physics, astrophysics, and condensed matter physics, emphasizing concepts like emergence and the study of extreme energy scales. 

Lecture 4 Black Body Radiation and Ultraviolet Catastrophe (Harris Chapter 2) (9/2/2026)

Starting with Lecture 4, we will focus on a cornerstone of quantum mechanics: wave-particle duality. We will examine how electromagnetic waves can behave like particles by studying blackbody radiation, the failure of the classical prediction, and Planck’s successful description of the spectrum. This introduces Planck’s constant h and the idea of quantized energy.

Lecture 5 Photoelectric Effect and Compton Scattering (Harris Chapter 2) (9/4/2026)

Lecture 5 examines the photoelectric effect and Compton scattering as a more direct evidence of the particle nature of light. The photoelectric effect shows that electrons are emitted only when the light frequency exceeds a threshold, and the kinetic energy depends on the frequency of light. Compton scattering further establishes that photons carry momentum and shows how conservation of energy and momentum leads to the wavelength shift and scattering angle.

Lecture 6 Q&A and Compton Scattering (Harris Chapter 2) (9/9/2026)

In Lecture 6, we'll take a moment to review the excellent questions raised by students. Afterward, I will walk you through the derivation of the Compton scattering formula.

Lecture 7 Q&A and Compton Scattering (Harris Chapter 2) (9/11/2026)

In Lecture 7, we explore when light acts as a wave versus a particle. It behaves like a particle when its wavelength is much smaller than the detector size, and like a wave otherwise. Slit experiments demonstrate that even individual photons build interference patterns over time, proving a particle's probability is directly linked to its wave amplitude.
(See also ai generated notes from Prof. Yongbin Feng)

Lecture 8 Matter Waves 1 (Harris Chapter 3) (9/14/2026)
Lecture 8 explores when matter exhibits wave-like behavior. We revisit the classic double-slit experiment, but this time, we substitute light with matter. 

Lecture 9 Matter Waves 2 (Harris Chapter 3) (9/16/2026)
In today's lecture, we'll look at another experiment that shows classical particles behaving like waves: electron beams creating diffraction patterns when fired at a crystal. After that, we'll dive into de Broglie's hypothesis, connecting a particle's wavelength directly to its momentum. To wrap up, we'll use a bit of educated guesswork to piece together what the wave function's governing equation might actually be. 

Lecture 10 Heisenberg's Uncertainty Principle (Harris Chapter 3) (9/18/2026)
In this lecture, I will introduce Heisenberg’s uncertainty principle. Before discussing it from a statistical perspective, we will first examine the Fourier-transform relationship between a wave described in the x-domain and its description in the k-domain. Using de Broglie’s relation between wave number and momentum, we will then see how the uncertainty principle naturally emerges from the wave nature of matter. 

Lecture 11 Heisenberg's Uncertainty Principle 2 (Harris Chapter 3) (9/21/2026)
In this lecture, we will continue our discussion of the Fourier transform by exploring a different perspective: interpreting A(k) as the amplitude when summing plane waves with varying wave numbers, k. Next, we will examine the uncertainty principle from a statistical standpoint. Finally, before concluding the chapter, we will briefly review the various interpretations of wave function collapse upon measurement. 

(Supplementary Material: Griffith's Chapter 1)

Lecture 12 Schrodinger Equation and Separation of Variables (Harris Chapter 5) (9/23/2026)
In this lecture, I will introduce the time-dependent Schrödinger equation (TDSE). As a first step toward finding solutions, we will apply the method of separation of variables to split the TDSE into two equations: a temporal equation governing the wave function's time dependence, and the time-independent Schrödinger equation (TISE) governing its spatial dependence. Lastly, I will demonstrate how these specific solutions correspond to stationary states.

Lecture:  Math Toolbox for the Schrodinger Equation (9/25/2026)

Lecture 13 Properties of a wave function and the Particle in a Box 1 (9/28/2026)
In this lecture, we will cover the essential properties of a wave function—specifically, that it must be continuous and smooth. Next, we will introduce the setup for the infinite square well. 

Lecture 14 Particle in a Box 2 (9/30/2026)
In this lecture, we will solve the particle in a box and appreciate what the solution means.

Lecture 15 Measurement Revisited with the Particle in a Box & Finite Potential Box  (10/2/2026)
Now that we have found the solutions for the infinite square well, we will revisit what happens when we make a position measurement of a particle. We will also use these solutions to revisit the statistical and probabilistic interpretation of quantum mechanics. Finally, we will move to the more realistic case of a finite potential well, where the potential barriers at the boundaries are no longer infinite.

Lecture 16 Finite Potential Box 2 and Simple Harmonic Oscillator  (10/5/2026)
In this lecture, we will continue our discussion of the finite potential well. We will then begin studying one of the most important model systems in quantum mechanics: the simple harmonic oscillator.

Lecture 17 Simple Harmonic Oscillator  (10/7/2026)
In this lecture, I will first re-emphasize why the simple harmonic oscillator is so important in quantum mechanics: it provides a useful approximation for many realistic physical systems. Although we will not solve the harmonic oscillator problem in detail (you will learn how to do so in PHYS 4307), we will take a brief look at its solutions and develop some physical intuition by comparing them with those of the infinite square well.

Special Guest Lecture: Compton Scattering Research at Argonne National Laboratory (10/12/2026)

In this special lecture, we will welcome Dr. Jarryd Horn from Argonne National Laboratory, who will join us remotely to discuss his research on using Compton scattering to study batteries. Following the presentation, we will have a short Q&A session where students can ask questions about his research, internship opportunities, and what it is like to work at a national laboratory.

Lecture 18 Expectation Values, Uncertainties, Operators, and Non-Stationary States (10/14/2026)

In this lecture, we will introduce expectation values and uncertainties to understand how quantum mechanics predicts the average outcomes and statistical spread of measurements. We will also discuss quantum mechanical operators, particularly the position and momentum operators, and how they are used to calculate expectation values. Finally, we will revisit stationary states and introduce non-stationary states, showing how the superposition of stationary states can lead to time-dependent probability distributions.