How much math is required to do QM?

[entropy1]

I write this post because there are some people that get irritated by my posts. I get why you do.

I think the signal I am getting in several threads of mine, is that you could try to understand QM through interpretations, but that the prerequisite is that you then also have to understand the math, and if you do, you will realize, like all physisists, that the math is the ultimate description of QM.

And I get that. Trying to do math without the math is not logical.

So Feynman and understanding QM: What do I gain by learning QM? Obviously something, because I am studying it and there are many physisists.

Ultimately, if doing math is the way to go with QM, there must be something that you learn from it. I wonder what. I understand that you have to do the math. But I think I am a bit of a philosipher too.

If QM is not about some ontology of the universe, but rather a way to predict physical measurement outcomes, it probably won't have much use for me.

I could resort to YouTube, but that is the other extreme.

PF decided not to facilitate philosophical discussions, which seem to be what I probably do want.

I am not against the math, but I read one book and learned the basics. I don't remember it anymore, but that could be enough right?

What would you recommend on literature?

 

[jedishrfu]

In modern physics courses, they teach the rudiments of Quantum Mechanics using the square well problem and showing how it relates to the energy levels of the hydrogen atom.

The math required to understand this of course is everything up to Calculus I, II and III and knowing Diff Equations as an extra helps too. For an upper level undergrad course in QM you'll need linear algebra and possibly boundary value problems.

In general, you'll have covered this level of math within the first two years of college.

 

[entropy1]

Could it be an idea to compile a collection of books PF recommends to study QM?

 

[entropy1]

In modern physics courses, they teach the rudiments of Quantum Mechanics using the square well problem and showing how it relates to the energy levels of the hydrogen atom.

The math required to understand this of course is everything up to Calculus I, II and III and knowing Diff Equations as an extra helps too. For an upper level undergrad course in QM you'll need linear algebra and possibly boundary value problems.

In general, you'll have covered this level of math within the first two years of college.

Is that roughly what you need do to participate on PF?

 

[Aidyan]

I always tell philosophers that without having at least an elementary understanding of the math they can't really understand QM. You don't need to learn all the stuff a physicists has to learn but the basics of calculus, linear algebra and statistics are necessary. Sort of the level that biologists or chemists learn would be ok. But you can't understand QM just by entertaining yourself with the plethora of interpretations of QM and which, BTW, I even consider not at all essential to understand QM. On the other side, true is also that a typical textbook on QM mostly focused on doing the math, will not furnish you the conceptual foundations of QM either, something which is essential for philosophers. Too much mathematical abstraction frequently obscures the conceptual foundations. So, to philosophers I always say try to find a middle way, do not avoid math but don't loose yourself in it either. Once you know what complex numbers and functions are, an integral, a differential equation, an eigenvalue equation, matrix representations, etc. are, then go over to a book which focuses more on the concepts. You will not regret it.

 

[entropy1]

[..]the basics of calculus, linear algebra and statistics are necessary. Sort of the level that biologists or chemists learn would be ok.[..]complex numbers and functions are, an integral, a differential equation, an eigenvalue equation, matrix representations, etc.

I've already had that, but thirty years ago and never had use for it. Three years ago I read Susskind, and forgot most of it. It was fun. I think I will just have to read it a second time. The diffulty level is not the problem. Thanks for reacting.

 

[DrClaude]

There is a lot of QM one can understand without calculus but only basic linear algebra. For that, one needs to use a "states first" approach, like in the book by McIntyre:
https://www.amazon.com/dp/0321765796/?tag=pfamazon01-20

 

[sysprog]

I think that in order to understand what we think about QM (I think that QCD is the closest to right on that we've arrived at) you should understand enough (abstract algebra) group theory to recognize the non-commutative SU(3) group.

 

[entropy1]

I think that in order to understand what we think about QM (I think that QCD is the closest to right on that we've arrived at) you should understand enough (abstract algebra) group theory to recognize the non-commutative SU(3) group.

Is there a good book on that? Group theory is very mysterious to me.

 

[entropy1]

There is a lot of QM one can understand without calculus but only basic linear algebra. For that, one needs to use a "states first" approach, like in the book by McIntyre:
https://www.amazon.com/dp/0321765796/?tag=pfamazon01-20

Susskind also starts with finite dimensional states and Dirac notation, but he let's it slide into infinite dimensional states. Very nice book for beginners actually!

Darn. I actually don't remember much about it anymore...

Thanks for reacting!

 

[sysprog]

Is there a good book on that? Group theory is very mysterious to me.

Abstract algebra is advanced mathematics, and QM is advanced physics -- I liked Fraleigh's book 'Introduction to Abstract Algebra', which winds up with an explanation of the general insolubility of the quintic.

 

[entropy1]

I am not sure if some of the people that react to me on PF mean to suggest that I should quit physics, or that they mean to say that I should participate only when I have a certain level of education in QM. Or that they mean that I don't understand a bit of QM yet or got it all wrong or am sloppy etc.

My aim was to get some global idea of how some issues I had with the matter work. I have some issues cleared up a little. However, PF is pretty strict about what you are allowed to discuss. I respect that.

I know contributants have done their best to inform and signal me, for which I am grateful.

I shouldn't say much more in this way.

Reaction not required.

 

[jedishrfu]

There's some other options:

1) Use Susskind's Quantum Mechanics the Theoretical Minimum

https://www.amazon.com/dp/B00FD36G1Q/?tag=pfamazon01-20

2) Zagoskin's Teach Yourself Quantum Mechanics Book

https://www.amazon.com/dp/B00RTY0JVK/?tag=pfamazon01-20

3) Non Nonsense Quantum Mechanics by Schwistenberg

https://www.amazon.com/dp/1790455383/?tag=pfamazon01-20

or you can follow the path of these folks:

 

[hutchphd]

I am not sure if some of the people that react to me on PF mean to suggest that I should quit physics, ...

Reaction not required.

.
Speaking strictly for myself, I think the more specific the question, the more useful is the answer. To ask a specific question indicates a lot of work on the part of the questioner. When that work has clearly been done, I am more than happy to make my very best effort to provide a useful answer. at the appropriate level or to suggest avenues for more general learning where required.

The two types of questions that I seldom bother with are:

1. some zealot with an agenda other than scientific inquiry
2. an idea that is, to paraphrase W Pauli, "not even wrong"

I am (so far) totally unfamiliar with your interactions here, so please do not particularize these comments. Keep working.

 

[sysprog]

To even more deeply steal from Pauli I might use 'not even close to wrong'.

 

[KevinMcHugh]

Is there a good book on that? Group theory is very mysterious to me.

Armstrong is awesome for group theory.

 

[jedishrfu]

I am not sure if some of the people that react to me on PF mean to suggest that I should quit physics, or that they mean to say that I should participate only when I have a certain level of education in QM. Or that they mean that I don't understand a bit of QM yet or got it all wrong or am sloppy etc.

My aim was to get some global idea of how some issues I had with the matter work. I have some issues cleared up a little. However, PF is pretty strict about what you are allowed to discuss. I respect that.

I know contributants have done their best to inform and signal me, for which I am grateful.

I shouldn't say much more in this way.

Reaction not required.

You can participate on PF at any level. It helps to roughly state the level upfront so that you don't get answers that are over your paygrade.

Usually we can tell by your questions where you stand but sometimes we get a newbie with some really deep question but without the necessary background to understand any of the answers and this leads to frustration on both sides.

The only thing we discourage here is fringe science so questions about some arcane unpublished theory are usually deleted and the poster warned. A common one was extending QM to paranormal phenomena which so fringe out there that we shutdown discussion immediately just like...

message terminated...

 

[strangerep]

@entropy1 : If you haven't already tried Greiner's "Quantum Mechanics -- An Introduction", give it a go. Greiner tends to explain the math hand-in-hand with the physics, with many fully-worked examples. I learned a LOT by self-studying his textbooks 20+ yrs ago.

 

[jedishrfu]

@entropy1 : If you haven't already tried Greiner's "Quantum Mechanics -- An Introduction", give it a go. Greiner tends to explain the math hand-in-hand with the physics, with many fully-worked examples. I learned a LOT by self-studying his textbooks 20+ yrs ago.

This is in stark contrast to Schiff who covered a lot by jumping from mountain top to mountain top with students left to traverse the lonely valleys without a guide to lead them.

Schiff was a popular QM book when I was an undergrad in the 1970's:

https://www.amazon.com/dp/B000OG2UB2/?tag=pfamazon01-20

https://en.wikipedia.org/wiki/Leonard_I._Schiff

I'm sure its been surpassed many times over.I often wonder if perhaps the book was written to be a reference book for physicists.

There was another book by Vladimir Rojansky that was also very popular in our physics department. I heard one story where someone bought a copy of his book in the second hand bookstore because they felt it was a shame for it to be there.

https://www.amazon.com/dp/0135016436/?tag=pfamazon01-20

https://en.wikipedia.org/wiki/Vladimir_Rojansky

I now see why as he was once a teacher and maybe a dept head at my college a decade before I got there.

 

[entropy1]

Speaking strictly for myself, I think the more specific the question, the more useful is the answer. To ask a specific question indicates a lot of work on the part of the questioner. When that work has clearly been done, I am more than happy to make my very best effort to provide a useful answer. at the appropriate level or to suggest avenues for more general learning where required.

I get that. In my case I have trouble taking up textual information, so doing extensive research is often asked to much. But I totally get what you're saying.