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I am a PhD math student, and I am wondering if I should study quantum mechanics while I don't have an undergrad background in physics.

I posted this question in physics stackexchange, but there doesn't seem to be many people interested in it there. In addition, I want to hear those who are just like me, math students who want to study theoretical physics and have difficulties with physics background (not to say also math background).

I actually studied computer science in undergrad. I switched to graduate math because I wanted to study quantum computing / information and in the long term to be involved more in quantum mechanics.

In the first two years of undergrad, I actually took general physics (physics for non-physicist students) courses: mechanics, thermodynamics, electromagnetics, modern physics. However, now 5 years later, I forgot most, not to say all, of them. Those courses obviously did not cover Lagrangian or Hamiltonian things, and taught very little (very insignificantly) about the Maxwell equations and the Schrodinger equation.

Now, I also don't know anything about partial differential equations, but I could take a graduate "Methods of Applied Maths" course in parallel with quantum mechanics.

Do I need to prepare more physics and mathematics before taking graduate quantum mechanics? What books should I use to prepare for those topics?

Have any mathematicians taken a quantum mechanics qualifying exam to get a multi-discpline degree?

Your experience and advice will definitely help me to decide if I should take the grad quantum mechanics course this coming semester.

Thank you.

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  • $\begingroup$ You should probably feel comfortable with basic material before proceeding to Quantum Mechanics at the graduate level. Math in QM includes a lot of linear algebra, as well as some more advanced material, like the representation theory of Lie Groups. Even if you have a handle on the math, physics isn't always formal, and you will certainly need to have a well-tuned intuition. It sounds like you mostly have the background, just brush up on the basics. $\endgroup$
    – rotskoff
    Jun 23, 2012 at 17:12
  • $\begingroup$ Ask your advisor. This is only worth it if you're sure you can write a thesis related to quantum mechanics; otherwise it's a waste of time that should be used for preparing for qualifying exams. $\endgroup$
    – Potato
    Jun 23, 2012 at 18:23
  • $\begingroup$ What was your field of study in Math in gra. math. level? Your answer will be different if you studied gemetrical fields or analytic or algebraic, graph theory, ... . $\endgroup$
    – AmirHosein Sadeghimanesh
    Jan 3, 2013 at 4:50
  • $\begingroup$ Depends on what you mean by "should". If you have to study it for your research, I suppose there is no question asked? Otherwise, if it is an interest, I would say no physics background is ok. For efficiency and clarity, you need to find a book that nails down to the mathematical foundations of QM while connecting to experiments. I just do not know any. Make a post to ask for that perhaps? $\endgroup$
    – Argyll
    Sep 16, 2014 at 1:36

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This answer is quite late, so I'll make it general for those wondering about how to jump into QM with an undergraduate or higher background in math. A word of caution to mathematicians entering the physics realm: though there is a great overlap in material, the emphasis, pedagogy, and approach of a physicist can be quite different than that of a mathematician. You may (or may not) be frustrated by the lack of rigor, and amount of "guesswork and validation" to find the solutions you are required.

The tools widely used in QM include:

  • differential equations / partial differential equations
  • linear algebra
  • vector operations / vector spaces
  • basic complex analysis

A great conceptual introduction to the physics of QM can be found here:

  • Wikipedia pages (Schrodinger Equation, Quantum Mechancs, and associated wiki links)
  • Introduction to Quantum Mechanics (David J. Griffiths).

The latter, in particular, I found quite exceptional. Though other texts may be more complete references, Griffiths makes the physical ideas behind QM very plain and intuitive - something often obscured elsewhere.

As for whether to take the undergraduate or graduate course: My experience is that the undergraduate course will focus more on the conceptual aspects of QM, while the graduate course will assume some of that and focus on more difficult problems; due to this, I personally would recommend beginning with the undergraduate course.

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Chemists and material scientists routinely get an exposure to QM without needing all the courses that a physicist takes. Math through multivar-calc/DiffyQs and first year physics is enough.

Take a look at the QM in a standard p-chem book (say Atkins). http://www.amazon.com/Atkins-Physical-Chemistry-Peter-W/dp/0198792859 pages 249-365

You don't need to learn QM as well as the physicist does or with all the unconscious assumptions of prerequisites. Half a loaf is better than none. You can work your way up to full loaf if worthwhile, later.

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I think Chris Isham's book would be right up your alley: https://www.amazon.com/Lectures-Quantum-Theory-Mathematical-Foundations/dp/B01K0RJQT8/ref=pd_sbs_14_1

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