Quantum Mechanics

These are my resources for getting through a year of quantum mechanics. I took my first two quarters (Winter & Spring 2021) completely virtually, and my last quarter in person (Fall 2021). I split up my stuff into each course: qm1, qm2, qm3/advanced qm. This course series was taught by Professor Jeffery Harvey.

These are the general topics covered in each course

QM1

1. Postulates of QM
2. Linear Algebra needed
3. 2 state systems
4. Stern Gerlach device
5. Entanglement
6. Schrodinger Equation (Time indp & Time dep)
7. 1D Problems
8. Simple Harmonic Oscillator
9. Coherent, scattering, tunneling states

Here are those lecture notes:

Lecture 1

Lecture 2

Lecture 3

Lecture 4

Lecture 5

Lecture 6

Lecture 7

Lecture 8

Lecture 9

Lecture 10

Lecture 11

Lecture 12

Lecture 13

Lecture 14

Lecture 15

Lecture 16

Lecture 17

Lecture 18

Lecture 19

Lecture 20

Lecture 21

Lecture 22

QM2

1. QM in 3D
2. Hydrogen Atom & Hydrogonic Atoms
3. Angular Momentum
4. Spin & Spin precession
5. Addition of Angular Momentum
6. Spin Statistics
7. Approximation methods (dimensional analysis, variation method, first & second order perturbation theory)

Lecture 1

Lecture 2

Lecture 3

Lecture 4

Lecture 5

Lecture 6

Lecture 7

Lecture 8

Lecture 9

Lecture 10

Lecture 11

Lecture 12

Lecture 13

Lecture 14

Lecture 15

Lecture 16

Lecture 17

Lecture 18

Lecture 19

Lecture 20

Lecture 21

Lecture 22

Addition of Angular Momentum

QM3 / Advanced QM

1. Density Matrices
2. Classical Error Correction
3. Quantum Error Correction
4. Toric Codes
5. Combining E&M with QM
6. Time Dependent Perturbation theory

Lecture 1

Lecture 2

Lecture 3

Lecture 4

Lecture 5

Lecture 6

Lecture 7

Lecture 8

Lecture 9

Lecture 10

Lecture 11

Lecture 12

Lecture 13

Lecture 14

Lecture 15

Lecture 16

Lecture 17

Lecture 18

Lecture 19

Lecture 20

Lecture 21

Lecture 22

Lecture 23

Lecture 24

Lecture 25

Griffiths

Griffiths Introduction to Quantum Mechanics is basically the OG, the classic, the needed undergrad Quantum Mechanics textbook. It has an appendix that covers the linear algebra needed. But it also jumps straight into Schrodinger’s Equation and doesn’t provide too much of motivation for QM as a whole. Once you get through the first couple chapters about wtf is going on and the discussion on probabilities, then the textbook is easy to read.

Shankar

Shankar’s Principles of Quantum Mechanics is Griffith’s older brother. This is the grad school Quantum Mechanics textbook. This is big boi time. Despite being at a higher level, the first chapter covering the math is very thorough. I mostly used this textbook to supplement Griffiths rather than its own standalone thing. The section on addition of angular momentum was particularly helpful.

Theoretical Minimum

This book was completely seperate from the course that I sought out. I used this as another supplemental material more for intuition of quantum mechanics as a whole rather than anything else. Another way to view qm.

Leonard Susskind is the author of the Theoretical Minimum book, which was actually written by a student from his lectures. The lectures were for returning adults coming back to learn physics in a special program through Stanford, so these aren’t technically geared towards undergrads in their early twenties. But it’s like the book, but hearing him say it and formulate general ideas. It’s only 10 lectures. They’re dense, but very helpful in gaining intuition.

3b1b

You know him, you love him, it’s him: 3Blue1Brown. The almighty youtuber of all things math on youtube. He has a great playlist on linear algebra which helped a lot in the initial understanding what the tools are for QM. He does some light calculations, but more important is the general idea of things like eigenvectors, eigenvalues, and matrix multiplication.