Educational Path to QM and QM Occupations

[Tristan Barrow]

Hi, my name is Tristan Barrow,

I know this forum has gotten a lot of questions like this but none of them really fit my particular needs so I thought I would ask it again.
Do the math subjects I am interested in lead me to Quantum Mechanics? If not what would be the best place for me given my passions (see below).

These are the subjects I find interesting. I simply devoured Calculus 1-Calculus 3 (Derivatives, Integrals, Vector Calculus, Sequences and Series, Partial Derivatives, and Double/Triple Integrals). While I was taking those I was grabbing Linear Algebra books from the library and reading them in my spare time and I was disappointed I couldn’t take the class on Differential Equations. From what I understand these are the subjects that will ultimately direct me to Quantum Mechanics. Is this correct? What else?

Secondly, I was wondering what kind of occupation I would have if I decide to do Quantum Mechanics. Quite frankly I don’t want to end up being a teacher for my whole life. I would like to have a long carrier first then later in my life become a teacher. So what kind of work is there for someone who does QM?

Thanks,
Tristan Barrow

 

[Jorriss]

What do you think it means to do QM?

 

[homeomorphic]

From what I understand these are the subjects that will ultimately direct me to Quantum Mechanics. Is this correct? What else?

Yes, that's pretty much all you would need to read the most basic quantum mechanics books, but you should probably study classical mechanics first. There are a lot of different perspectives on quantum mechanics, some of which require that minimal background, whereas some other points of view would probably require something like a PhD in math. What approach you would take would depend on whether you wanted to be more like a mathematician who does physics-inspired math or whether you want to do the minimum math required to be able to make a contribution.

Secondly, I was wondering what kind of occupation I would have if I decide to do Quantum Mechanics. Quite frankly I don’t want to end up being a teacher for my whole life. I would like to have a long carrier first then later in my life become a teacher. So what kind of work is there for someone who does QM?

Normally, people don't go around calling it "doing QM". They just call themselves physicists, condensed-matter physicists, particle physicists, etc.

Most people who study physics will probably not end up doing physics and have to switch to something else entirely, preferably something that takes advantage of mathematical and programming skills they learned as a byproduct of studying physics. If the goal were only to get one of these sorts of programming/mathematical/statistical jobs, it would be far more efficient to just study for those particular jobs. Some people have goals other than just employment, though, and that's fine, but just make sure you don't end up like me and put everything into just pursuing your curiosity and nothing (except by chance) into employability because then, you'll have a very rough career change in store for you if things don't work out.

So, there isn't that much work out there where you do physics outside of being a professor or working at a national lab or something like that, and all of that stuff is pretty competitive, so you'd have to get lucky to keep doing it, beyond grad school or a postdoc or two. There are some physicists who work for companies, but you'd have to develop certain skill sets if you wanted to do something like that, like maybe semi-conductor physics, if you wanted to work for the computer industry, helping to design the next generation of computers or something like that.

 

[Geometry_dude]

Well, the mathematics you described is pretty much the basis you need in any field of physics. Ordinary and partial differential equations are really important in physics as well, so I recommend taking those courses. Also try to get a course in group theory.

If you are more mathematically inclined and really wanted to understand the math you are going to hate quantum mechanics and quantum field theory one day upon realizing that most of it is done in a very non-rigorous, intuitive fashion (unless you go down the mathematical physics path where you're pretty much unemployable outside of academia).

Quantum mechanics is really old and it appears to me that you have to get into the more advanced stuff in that direction (quantum field theory, gauge-theories,...) if you want to go up in academia. I would, however, recommend to stay open minded until you got the degree you want.

 

[Tristan Barrow]

Thank you for answering my questions. I apologize for my ignorance of the subject (Doing QM... ).

I want to do more math than physics, but when I was browsing the web and saw that all of the math subjects I wanted to learn about could lead me to Quantum Mechanics, my childhood romanticism kicked in and I had to find out if it was really true and how realistic it was. If I understand you guys correctly, it is realistic however, it would lead me directly to academia which I would like to avoid for a while.

I am trying to keep an open mind about it but what I would love to do is have an occupation that allows me to work daily with all of the aforementioned math subjects (and some) in a rigorous fashion, without relying academia. Homeomorphic touched on this but do you have any more suggestions for me?

Thank You,
Tristan Barrow

 

[homeomorphic]

If you are more mathematically inclined and really wanted to understand the math you are going to hate quantum mechanics and quantum field theory one day upon realizing that most of it is done in a very non-rigorous, intuitive fashion (unless you go down the mathematical physics path where you're pretty much unemployable outside of academia).

Actually, the reason I got a math PhD, rather than physics, was that I thought it was more intuitive and conceptual, whereas physicists seemed to be more into calculation and less into concepts than the mathematicians. It didn't have much to do with lack of rigor, although, I suppose that was a bonus when I was deciding on grad school because I was just getting into rigorous math and was really into having both rigor and intuition at that stage. The PhD actually made me care less about rigor, oddly enough, because you can't really get anything done in topology if you try to be 100% rigorous (except when you're studying the simpler beginner's stuff).

Anyway, I thought I could get away with trying to do both math and physics, but very few people can really do that these days, with both subjects getting to be so complicated, and the structure of academia doesn't really allow for you to learn 2 PhDs worth of stuff before you're expected to start cranking out papers like a madman. It's hard to appreciate the vast scale of these theories and the time it will take to learn everything, until you're in the thick of it.

To Tristan: there aren't that many jobs where you just get to do that much math outside of academia. I just finished a PhD in math and trying to find something that fits my skill set outside of academia is like searching for a needle in a haystack. The stuff I did for my PhD is pretty obscure, but still, if you look through a random course catalog for undergraduate math, I'd probably know every subject taught, except one or two, so you'd expect that this would help me to get a job somewhere, but it doesn't really, by itself. As a math prof I was talking to about jobs said, they will just look at the math and say "check". But that's just one of their check marks out of many. By itself, it's not worth that much. That should give you more of a feel for most industry jobs, unless you sort of shoot the moon and land one of the few pure research jobs out there or something.

You might want to think about engineering (in which most jobs probably don't use that much math, but some will--although, you'd use lots of calculus/diff eq while getting an engineering degree). Possibly computer graphics, but I don't know how good the market is for that, particularly for the more mathematically-intensive aspects of it. Another possibility might be some kind of financial job. Or statistics. Or data science. Machine-learning is a pretty big thing these days, and it can involve a fair amount of math, potentially, but I'm not sure, in practice, for most jobs out there, that it will be that much. Computer vision and image-processing. Might be some market for that. Programming is a really good skill to have if you want to avoid academia (and even in academia, in some cases). Also, you might want to look into industrial engineering/operations research.

 

[heatengine516]

Hi, my name is Tristan Barrow,

I know this forum has gotten a lot of questions like this but none of them really fit my particular needs so I thought I would ask it again.
Do the math subjects I am interested in lead me to Quantum Mechanics? If not what would be the best place for me given my passions (see below).

These are the subjects I find interesting. I simply devoured Calculus 1-Calculus 3 (Derivatives, Integrals, Vector Calculus, Sequences and Series, Partial Derivatives, and Double/Triple Integrals). While I was taking those I was grabbing Linear Algebra books from the library and reading them in my spare time and I was disappointed I couldn’t take the class on Differential Equations. From what I understand these are the subjects that will ultimately direct me to Quantum Mechanics. Is this correct? What else?

Secondly, I was wondering what kind of occupation I would have if I decide to do Quantum Mechanics. Quite frankly I don’t want to end up being a teacher for my whole life. I would like to have a long carrier first then later in my life become a teacher. So what kind of work is there for someone who does QM?

Thanks,
Tristan Barrow

Those subjects you listed are the core math subjects required to start doing physics at the junior/senior level. Generally, classical mechanics and electrodynamics give you the prerequisite physics knowledge to start QM. The Hamiltonian principle(classical mechanics) is vital for QM. Linear algebra is also super important for QM.

As far as occupations, you don't really do research/work in QM. It's a subject. Condensed matter physics uses lots of QM. Working in quantum information/quantum computing would also be fairly close to a "QM occupation," especially if you do research in something more applied like quantum error correction or quantum cryptography.