Syllabus

Textbook Used: 1) Introduction to Quantum Mechanics by David Griffiths and Darrell F. Schroeter 2) Modern Quantum Mechanics by J.J. Sakurai and Jim Napolitano 

Lecture 2 Appreciation of the Schrodinger Equation
The Schrödinger equation can look daunting, but once we look past the notation, there are a couple of things you will come to appreciate. Also, it is a good time to review the nice property called superposition principle of a linear differential equation. 

Lecture 3 Double Slit Experiment and the Born Interpretation

The double-slit experiment demonstrates that matter possesses wave-like properties. We will discuss the core insights gained from observing particle interference and examine why quantum mechanics relies on probability rather than certainty. 

Lecture 4 Consistency of the Schrödinger equation and the Born Interpretation

Are the Born interpretation and the Schrödinger equation consistent with one another? Is probability conserved? Building on the role of probability in quantum mechanics, we will learn how to calculate expectation values in quantum mechanics.

Lecture 5 Stationary waves as solutions of the Schrödinger equation

In quantum mechanics, applying the separation of variables to the Schrödinger equation produces stationary state solutions, where the probability density remains constant over time. 

Lecture 6 More discussion of stationary waves and the Infinite Square Well (ISW)

After exploring the properties of stationary states in greater detail, we will begin our analysis of the infinite square well. 

Lecture 7 More on solving the Infinite Square Well

After completing our analysis of stationary states in the infinite square well, we will transition to more general wave solutions. Pay attention! The general waves part go beyond the typical scope of Modern Physics! 

Lecture 8 Invitation to Quantum States: A little taste of the Uncertainty Principle and the Stern-Gerlach Experiment 1

The uncertainty principle can be viewed from the perspective of Fourier transformations. This invites us to think and transition from working solely with wavefunctions to the broader framework of quantum states. The Stern-Gerlach experiment provides the perfect machinery for understanding this shift. 

Lecture 9 Stern-Gerlach Experiment 2

When we observe the Stern-Gerlach experiment in sequence, it behaves similar to that of a polarizing filter. What does this analogy reveal about the nature of quantum states and the process of measurement in quantum mechanics? 

Lecture 10 Formalism 1

Now it is really time to learn seriously about quantum states and operators. Let us learn the mathematical structure. This may seem boring but it is super important! (Warning: students have always mentioned this is the most difficult part of the course in the past surveys).

Lecture 11 Formalism 2 and the Postulates of Quantum Mechanics

Now that we have the math under our belts, we can finally apply it to physics. We will begin with the postulates of quantum mechanics—the fundamental rules that serve as the bedrock, or the constitution, of the entire field. 

Lecture 12 Using Matrices in Quantum Mechanics

Mastering quantum mechanics involves more than just solving differential equations. You will also learn to represent physical states as abstract vectors and observables as matrices. 

Lecture 13 A little more matrices and the Quantum Harmonic Oscillator(Agebraic Method)

There is a saying: If you receive your diploma and can’t solve the quantum harmonic oscillator on the back of it, you should probably hand it back!

Lecture 14 Continuous spectra and the Quantum Harmonic Oscillator 2 (Algebraic Method) 

1. What if your eigenvalues are continuous? 2.There are two ways to attack the harmonic oscillator, one is the algebraic method.

Lecture 15 Harmonic Oscillator 3 (Algebraic Method) 

Lecture 16 Harmonic Oscillator 4 (Analytical Method)

There is another way to solve the harmonic oscillator. This method is a bit more boring but the same method will be used later again so pay attention. 

Lecture 17 Harmonic Oscillator 5 (Analytic Method)

Lecture 18 Free Particle

When the potential V is zero everywhere, the math seems straightforward. But beneath that simplicity lies a deeper complexity: the transition from discrete states to a continuous spectrum, which we learned previously. Let’s explore why the free particle isn't as simple as it looks.

Lecture 19 Compatible Obervales and the Generalized Uncertainty Principle

Did you know that a non-zero commutator [A, B] is the mathematical 'smoking gun' for some of the most famous effects in quantum mechanics? It tells us that A and B has its own version of the generalized uncertainty principle similar to the one for x and p. 

Lecture 20 3D Schrodinger Equation in 3D

We will now generalize the Schrödinger equation to three dimensions, focusing on spherical coordinates. While the math of doing separation of variables may seem messy and intimidating, there is a major advantage: as long as the potential depends only on the radial distance r, a large portion of the solution remains identical across different systems. 

Lecture 21 Angular Part of the 3D Schrodiger Equation

Let us look deeply into the angular part of the Schrodinger equation.

Lecture 22 Radial part of the 3D Schrodinger Equation and the Hydrogen atom

Unlike the angular components, the radial wavefunction depends directly on the form of the potential V(r).  We will now explore the most fundamental and elegant example in all of physics: the Hydrogen atom. Its successful derivation remains, arguably, the greatest triumph of quantum mechanics. 

Teaching Evaluations from students