Syllabus

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 Stern-Gerlach Experiment 1

The Stern-Gerlach experiment provides the perfect machinery for understanding quantum states.

Lecture 6 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 7 Bra and Kets

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 8 Orthogonal Eigenstates and Real Eigenvalues, Matrices

Remember! A measurement in the lab is a real number. What are the requirements of the math used in quantum mechanics? Also, can we represent quantum mechanical vectors and operators into matrices?

Lecture 9 Matrices in Quantum Mechanics and Back to Schrodinger Equation

Lecture 10 Time Independent Schrodinger Equation and Stationary Waves

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 11Infinite Square Well 1

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 12 Infinite Square Well 2 and the Harmonic Oscillator

Lecture 13 Quantum Harmonic Oscillator 2 (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 3 (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 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 16 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 17 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 18 Delta Potential

A delta potential is significant because it is the simplest model of an extremely localized interaction that can still scatter a particle, create a bound state, and impose a jump condition on the wavefunction’s derivative. 

Lecture 19 Delta Potential 2

Lecture 20 Scattering States in Finite Potential and Uncertainty Principle

Lecture 21 Energy Time Uncertainty Relation and 3D Quantum Mechanics

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 22 Separation of Variables Spherical Harmonics and Angular Momentum

Let us look deeply into the angular part of the Schrodinger equation. This has relations with the angular momentum operators.

Lecture 23 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. 

Lecture 24 Radial part of the 3D Schrodinger Equation and the Hydrogen atom 2

Lecture 25 Angular Momentum Operator

Teaching Evaluations from students