Quantum Mechanics (Intro): Skills, Attitudes & Habits

[raj_vad]

hi
I am working on a project on cultural aspect of science.

I would like to know what you feel about

(a) which skills are inculcated in a student of Quntum MEchanics (intorductory) course?

(b) what attitudes and habits are likely to be developed in a student of QM (intro) course?

YOur opinion would be of great use to me.

Thanks

RVV

 

[vanesch]

hi
I am working on a project on cultural aspect of science.
I would like to know what you feel about
(a) which skills are inculcated in a student of Quntum MEchanics (intorductory) course?
(b) what attitudes and habits are likely to be developed in a student of QM (intro) course?

(a) unless he continues in some very specific domains, no useable skills what so ever result from following an intro course in QM

(b) the feeling of superiority over the rest of (ignorant) humankind, by knowing what others don't and knowing that everything is uncertain...

 

[SpaceTiger]

(a) which skills are inculcated in a student of Quntum MEchanics (intorductory) course?

Depends on the teacher. I came out of QM being more proficient with linear algebra and diff. eq., but not knowing much more about physics. I had to look elsewhere to learn the concepts behind QM. For general purposes, I'd say the only thing a standard QM course teaches is discipline.

(b) what attitudes and habits are likely to be developed in a student of QM (intro) course?

In the traditional course, I'd say one develops the habit of becoming disconnected from the physical nature of things. There is so much focus on the math that it's very easy to lose touch with nature. That's not to say, however, that the study of QM is, in of itself, disconnected from nature, just that the courses tend to steer students in that direction.

Also, it was definitely one of those courses that discouraged some of the less mathematically-inclined students from studying physics. In some cases, that was a good thing. In others, I'm not so sure. Some of the greatest physicists of the last two centuries had only basic mathematical skills, so it's not clear to me that we should be culling out people who aren't skilled with linear algebra.

EDIT: Changed "decades" to "centuries". I do suspect there are successful physicists from the past two decades that aren't very skilled with math, but I'm not prepared to name them.

 

[siddharth]

Some of the greatest physicists of the last two decades had only basic mathematical skills

That is interesting. Can you name a few, so that I can find out more about them?

 

[SpaceTiger]

That is interesting. Can you name a few, so that I can find out more about them?

Michael Faraday is the first one that comes to mind. My E&M professor liked to talk about how he didn't understand the equations behind gauss' law, but could picture it with field lines and imaginary surfaces. I've heard about various others (all experimentalists, I believe), but I don't remember their names at the moment. When exam periods are over, perhaps I'll look into it further.

Don't get me wrong, I'm not supporting these crackpots who try to come up with a theory of everything using only algebra. I'm pretty sure a theorist couldn't get by with only lower-level mathematics. I'm just saying that physics is more dependent upon physical intuition than many of the courses let on, especially quantum mechanics. Sifting out students because they're not talented mathematicians may not be the best idea.

 

[Gokul43201]

Michael Faraday is the first one that comes to mind.

I guess you meant last 2 centuries. I find it hard to imagine a successful physicist from the last few decades that was weak in math.

 

[SpaceTiger]

I guess you meant last 2 centuries.

Yeah. Edited.

I find it hard to imagine a successful physicist from the last few decades that was weak in math.

Why? What are you considering to be "weak in math"? Observational cosmologists, for example, almost never need linear algebra and usually use only basic differential equations. My E&M professor here at Princeton openly admitted that he wasn't all that mathematically adept and that most of his time was spent conducting experiments. His knowledge seemed to be at the level of Jackson E&M.

Clearly, more math is needed than was 200 years ago, but it's certainly not the case that experimental/observational physicists need to be skilled mathematicians.

 

[Gokul43201]

Observational cosmologists, for example...

Oh, I was only talking about physicists !

 

[franznietzsche]

Oh, I was only talking about physicists !

Zing!

If you can't handle at least multivariable and vector calculus you can't do much of modern physics.

 

[raj_vad]

By-products of QM studies

Does the study of QM helps in theory-building?

Does the study of Hilbert spaces or infinite dimesnional spaces give you any new insights in solving a problem?

Does it make you see symmetries in a new way?

I would like to know some of these experiences.
The discussion seems to have go lil awry, I am afraid.
I wish I could make it more focussed.
Thanks a lot space-tiger and all of you.

 

[vanesch]

Does the study of QM helps in theory-building?

Does the study of Hilbert spaces or infinite dimesnional spaces give you any new insights in solving a problem?

Does it make you see symmetries in a new way?

I would like to know some of these experiences.
The discussion seems to have go lil awry, I am afraid.
I wish I could make it more focussed.
Thanks a lot space-tiger and all of you.

Ah, sorry, and I contributed to it. "general discussion" is the (only) place on PF were people are not supposed to be really serious. This is the joker's place a bit...

But my answer was not so very silly either, and was a bit in the same spirit as space tiger. A *usual* intro course in QM does not learn you much physical insight, because it focusses on getting the formalism working. But then, even there, you do not get far enough to be able to use it to tackle a "real" problem ; usually an intro QM course ends with the working out of the hydrogen atom.
The main things you've done is A LOT of linear algebra (that's useful as a skill) and some partial differential equations (that's also useful elsewhere). The physics usually remains entirely opaque, and that's meant to be, because no matter how you view QM, it is mindboggling. But that insight comes much later, because in order to even perceive it, you have to become fluent with the machinery.
The only ILLUSION you get out of solving the hydrogen atom is that you now "know" how to deal with chemistry in a physicist's way. But BZZT. Once you start doing such a thing, as say, H Cl, you are dealing with such a difficult problem that it is even hard to get good numerical estimates.
That's why I said that after an *intro* course, you might have the illusion that you can now go and beat that silly chemistry professor to the ground... well, no. A genuine QM problem is usually practically unsolvable. But as you haven't seen that yet in the intro course, you might think that there exist methods (such as finite element in classical mechanics) that can solve real-world problems. They are usually *much harder* than you anticipate after an intro course.

So, usually, you get out:
- a piped-up set of math skills
- not much physical insight (yet)
- the illusion of being able to do things with it.

Nevertheless, the genuine skill you do get out is the first one.

At least that has been my experience, but I think it is quite general.

 

[raj_vad]

Wich is a better place on PF


Thanks Vanesh,
Can you tel me which place in PF is approprate for a discussion like this?

 

[SpaceTiger]

Oh, I was only talking about physicists !

Well, it's good to know you weren't making a serious point.

Nearly anybody can learn to do mathematics, but that doesn't make them a skilled mathematician. My point was not that students should be given less competence in mathematics, but rather that they shouldn't be given the impression that physics is just about math and that they won't be happy making a career out of it if they're not skilled mathematicians. They still need to work and develop the skills relevant to their field, but there is much more to quantum mechanics (for example) than linear algebra and differential equations.