How to prepare for the Quantum Mechanics course?

[bacte2013]

Dear Physics Forum personnel,

I am a college student with double majors in the mathematics and computer science. I recently got interested to the art of quantum mechanics course through my current undergraduate research in the theoretical computer science, where my near-future project will involve the quantum mechanics and its applications to the computation theory and cryptography. After discussing with my research advisor, I decided to take the course in a quantum mechanics and enrolled to the course at my university.

Unfortunately, my only background is in AP Physics, which I took three years ago. So I am unfortunately not familiar with many concepts in the modern physics, let alone the general physics. I decided to use the rest of this semester and the Winter Break to prepare for the quantum mechanics course that I will be taking on the next semester. Could you give me some advice and tips on how to prepare for it? What should I study? Can I directly jump into the quantum mechanics? If I can jump directly to the quantum mechanics, is there a book or two that teaches the classical mechanics and other necessary prerequisites beforehand?

As for the mathematical background, I am currently taking the Analysis I (Rudin-PMA), Linear Algebra (Friedberg), and Discrete Mathematics (level of Rosen).

I included a link for the quantum-mechanics course I enrolled (offered in every Spring):
https://www.physics.wisc.edu/academics/spring2015/531

Thanks,

 

[micromass]

Familiarity with classical mechanics is definitely necessary. This means the Hamiltonian formulation of mechanics.

 

[jtbell]

Hmm, let's look at the prerequisites for Physics 531. The course descriptions can be found by following links under the "Undergraduate" menu on the link that you gave.

Physics 311 is Mechanics. It uses the book by Marion and Thornton. Prerequisite is the first-year calculus-based General Physics course. Definitely above AP Physics level.

Physics 322 is Electromagnetic Fields. It uses the book by Griffiths. Prerequisite is 311. Also above AP Physics level.

Plus "a course in modern physics", which I suppose might mean either 205 which uses Tipler's "Elementary Modern Physics", or 241 which uses Tipler's "Modern Physics". These appear to be different books, even though they're both by Tipler. Both of those courses assume General Physics as pre-requisite.

We teach QM here using Griffiths, also. The pre-requisite is our calculus-based General Physics course, three semesters which includes introductory modern physics, plus the full calculus sequence and differential equations, but not linear algebra. We introduce the LA concepts as needed, which isn't ideal, but we're a small college that offers the upper-level courses only every second year, and too many prerequisites makes scheduling difficult. But you have linear algebra anyway.

So... I'm skeptical about taking 531 with only high-school AP Physics under your belt. I'm not going to say it's impossible, but it's a stretch. At least get a copy of their General Physics and Modern Physics books so you can brush up on them. In the Modern Physics book, focus on the treatment of basic quantum physics and the Schrödinger equation. It will probably do the "particle in a box" in some detail, and the simple harmonic oscillator in less detail. It will help to have at least seen those beforehand so you won't be starting completely from scratch.

Familiarity with classical mechanics is definitely necessary. This means the Hamiltonian formulation of mechanics.

No, full-on Hamiltonian mechanics shouldn't be necessary, even though Marion and Thornton do cover it. I checked the index of my copy of Griffiths to reassure myself that my memory is correct. As far as I can tell, he uses "Hamiltonian" only for the name of the operator or quantity which represents the sum of potential and kinetic energy, and doesn't go any deeper than that. Most introductory QM courses in the US are like this, as far as I know.

 

[bacte2013]

H\

Hmm, let's look at the prerequisites for Physics 531. The course descriptions can be found by following links under the "Undergraduate" menu on the link that you gave.

Physics 311 is Mechanics. It uses the book by Marion and Thornton. Prerequisite is the first-year calculus-based General Physics course. Definitely above AP Physics level.

Physics 322 is Electromagnetic Fields. It uses the book by Griffiths. Prerequisite is 311. Also above AP Physics level.

Plus "a course in modern physics", which I suppose might mean either 205 which uses Tipler's "Elementary Modern Physics", or 241 which uses Tipler's "Modern Physics". These appear to be different books, even though they're both by Tipler. Both of those courses assume General Physics as pre-requisite.

We teach QM here using Griffiths, also. The pre-requisite is our calculus-based General Physics course, three semesters which includes introductory modern physics, plus the full calculus sequence and differential equations, but not linear algebra. We introduce the LA concepts as needed, which isn't ideal, but we're a small college that offers the upper-level courses only every second year, and too many prerequisites makes scheduling difficult. But you have linear algebra anyway.

So... I'm skeptical about taking 531 with only high-school AP Physics under your belt. I'm not going to say it's impossible, but it's a stretch. At least get a copy of their General Physics and Modern Physics books so you can brush up on them. In the Modern Physics book, focus on the treatment of basic quantum physics and the Schrödinger equation. It will probably do the "particle in a box" in some detail, and the simple harmonic oscillator in less detail. It will help to have at least seen those beforehand so you won't be starting completely from scratch.



No, full-on Hamiltonian mechanics shouldn't be necessary, even though Marion and Thornton do cover it. I checked the index of my copy of Griffiths to reassure myself that my memory is correct. As far as I can tell, he uses "Hamiltonian" only for the name of the operator or quantity which represents the sum of potential and kinetic energy, and doesn't go any deeper than that. Most introductory QM courses in the US are like this, as far as I know.

Dear Professor jtbell,

Thank you very much for the detailed advice! Before observing your and Professor Micromass's replies, I was at the Physics Library searching for good books to learn the quantum mechanics. I found that "Shankar's Principles of Quantum Mechanics" and "Zettili's Quantum Mechanics: Concepts and Applications" to be a perfect match for me as it covers the necessary background in the mathematics and classical mechanics in the first two chapters (especially the Shankar; I actually like it very much). My initial plan is to study those two chapters very closely and jump right into the QM chapters of Shankar. I chose that method as my rule-of-thumb in the book reading is to just jump right into the books of my interest and learn the necessary prerequisites as I go, but I see that my method may not be a best choice from your advice.

I was thinking about reading books on the general physics and modern physics, but I am not sure if that will be a good idea given that I have approximately two months to prepare for the QM course. So my plan is to read the books like Schaum's College Physics or prep books for AP Physics C to learn the general physics and read the relevant sections of QM in the modern physics alongside Shankar. Will this be a good plan? Or can I just jump directly to Shankar? Do I need to read separate books on the classical mechanics and electromagnetism?

I am really, really interested in the quantum mechanics, and I want to take the course for my interest and my undergraduate research. I would do my best to prepare myself for it.

 

[bacte2013]

Bump bump bump...

 

[one]

Why don't you talk to your professor? The person teaching the class will know best what is required. Also since you don't have the prerequisites you will probably need to ask their permission anyways

 

[jtbell]

Why don't you talk to your professor? The person teaching the class will know best what is required.

This.

Even if your university's registration system let's you enroll in the course without having completed the stated prerequisites, and without the instructor's explicit permission (which is required at my college if the prerequisites aren't satisfied), you should contact the instructor and ask for advice about your situation. He is the best source of information about how he is going to teach the course and what he expects from his students. (Correct the gender if necessary.)

In a post from last August, I find you asking about theoretical multivariable calculus books, even though you hadn't taken a Calculus III type course previously. I hope you have some experience with partial derivatives by now. You'll need it almost from the beginning, in order to deal with Schrödinger's equation.

If you have the typical mathematician's desire for logical rigor in the development of a subject, you probably won't find it in this course. Physicists usually learn and teach a subject in a practical fashion, taking some things "on faith" in introductory courses and filling gaps later in more advanced courses.