How to actually understand a topic

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Discussion Overview

The discussion centers around the challenges of achieving a deep understanding of physics topics, particularly quantum mechanics, despite strong mathematical skills and high exam scores. Participants explore the nature of understanding in physics, the role of intuition, and methods to build physical insights.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses feelings of inadequacy in understanding physics deeply, despite performing well academically, and questions how to build physical intuition.
  • Another participant suggests that some aspects of physics, especially quantum mechanics, may inherently lack intuitive understanding and rely more on mathematical logic.
  • Several participants discuss the notion of "impostor syndrome," suggesting that feelings of inadequacy may be common among students.
  • One participant emphasizes that teaching a topic is a sign of understanding, and acknowledges their own struggles to connect concepts across problems.
  • Another participant notes that gaining familiarity with physics concepts takes time and experience, and that self-doubt can be a part of the learning process.
  • Some participants propose that working through derivations, such as that of the Schrödinger equation, can enhance understanding by clarifying underlying assumptions.
  • There is mention of a specific paper discussing Feynman's derivation of the Schrödinger equation, indicating interest in foundational approaches to quantum mechanics.
  • One participant reflects on their research requiring deeper understanding of quantum mechanics and expresses a desire to improve their grasp of the subject.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to understanding physics deeply. Multiple views are presented regarding the nature of understanding, the role of intuition, and the challenges faced in learning complex topics.

Contextual Notes

Participants acknowledge that deep understanding in physics often requires time and experience, and that initial courses may not provide the comprehensive insight needed to teach the material. The discussion reflects a range of personal experiences and approaches to learning physics.

R.P.F.
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Hello,

I am a math and physics double major. But somehow I feel that it is very difficult for me to get a deep understanding of some topics in physics. I get all the mathematical muscles needed to solve problems and I score the highest on the exams. But I feel that I am actually faking it. I get this feeling all the time when I was taking quantum. I do not see the underlying physics behind the problem. Is that a way to understand a topic thoroughly and build up physical intuitions? Thank you very much.
 
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Could it not be that some things in physics, especially quantum mechanics, are just incredibly difficult to picture in your head and completely non-intuitive. A lot of physics cannot easily be built from intuition for this reason, and mathematical logic is the only way to proceed.
 
micromass said:
Hi R.P.F.! :smile:

Are you sure it's not just http://en.wikipedia.org/wiki/Impostor_syndrome because judging from your post, it looks like that...

Hi! But..I feel that one only has a good understanding of a topic when he can teach it. I am definitely not good enough to teach, say, quantum. If you throw me a problem then I can do it. But I cannot connect ideas between problems. I guess I'll have to work on more problems. ╭(╯^╰)╮
 
JesseC said:
Could it not be that some things in physics, especially quantum mechanics, are just incredibly difficult to picture in your head and completely non-intuitive. A lot of physics cannot easily be built from intuition for this reason, and mathematical logic is the only way to proceed.

That is also true. But I want to understand quantum so badly...
 
Well, you're not supposed to be able to teach it during your first course. You take it once, get some familiarity with the equations and concepts. Then you take more courses which draw on that material, use the material in your own research, see those equations come up in practice in research papers, etc. Your understanding should keep growing over time and eventually you may be able to teach it. Talking to others about it helps a ton too (this forum is good for that).

Also I'm sure a lot of professors who seem to know everything were not so proficient in their first semester of teaching the course.

IMO, science is very complicated and many aspects of it are subtle. It's better to constantly doubt yourself and question your understanding than to be one of these people who just doesn't seem to realize that they are oversimplifying things. Just always try to break a problem down to the elements that you're really sure about, even if that doesn't seem like much.
 
R.P.F. said:
Hello,

I am a math and physics double major. But somehow I feel that it is very difficult for me to get a deep understanding of some topics in physics. I get all the mathematical muscles needed to solve problems and I score the highest on the exams. But I feel that I am actually faking it. I get this feeling all the time when I was taking quantum. I do not see the underlying physics behind the problem. Is that a way to understand a topic thoroughly and build up physical intuitions? Thank you very much.

I think if you can get that kind of understanding in one course, you're either very intelligent, or you have a great teacher or both.

If you can do that, then great. But its just not possible to know all the nooks and crannies and put so many things into context like a professor (or some expert) can. Also don't feel bad about that, because it takes people years and years of their life to get to that stage.

Also since you are saying you are doing a math double major, I think its being a bit hard on yourself to have deep knowledge about math or physics let alone both of them. One thing you should remind yourself is that the stuff you are learning has been done by many dozens (if not hundreds or thousands) of people, all who are very smart, and all who have spent a lot of time to contribute in some small way to the body of knowledge that we take for granted. When you put that into perspective, I think it doesn't make sense to be hard on yourself.

Keep at it, and things will come.
 
R.P.F. said:
Hello,

I am a math and physics double major. But somehow I feel that it is very difficult for me to get a deep understanding of some topics in physics. I get all the mathematical muscles needed to solve problems and I score the highest on the exams. But I feel that I am actually faking it. I get this feeling all the time when I was taking quantum. I do not see the underlying physics behind the problem. Is that a way to understand a topic thoroughly and build up physical intuitions? Thank you very much.

Did you try working on derivations of your favourite theories, for example: a derivation of the Schrödinger equation? This can help you gain more insight/understanding into the assumptions that go into an equation. Personally this is the only way for me to study physics on a deep level, and I enjoy it a lot!
 
You can derive the Schrödinger equation?
 
  • #10
For example: I have on my desk now the paper "Feynman's derivation of the Schrödinger equation" by David Derbes (Am. J. Phys. 64 (7), 1996). It says that "many of the standard techniques of quantum field theory derive from [it]".
 
  • #11
johng23 said:
You can derive the Schrödinger equation?
Yeah you can if you start from some other point of QM. One way is to start out with which commutator relations you want to hold and from that derive the equation.
 
  • #12
johng23 said:
Well, you're not supposed to be able to teach it during your first course. You take it once, get some familiarity with the equations and concepts. Then you take more courses which draw on that material, use the material in your own research, see those equations come up in practice in research papers, etc. Your understanding should keep growing over time and eventually you may be able to teach it. Talking to others about it helps a ton too (this forum is good for that).

Also I'm sure a lot of professors who seem to know everything were not so proficient in their first semester of teaching the course.

IMO, science is very complicated and many aspects of it are subtle. It's better to constantly doubt yourself and question your understanding than to be one of these people who just doesn't seem to realize that they are oversimplifying things. Just always try to break a problem down to the elements that you're really sure about, even if that doesn't seem like much.

Thank you! I just get started on my research which requires a deeper understanding of quantum than i currently have, so I'm working on it.
And yes the easiest way to derive the SE is to use the relation between the time-evolution operator and the Hamiltonian. I only know how to do it for a pure state though.
 
  • #13
Sybren said:
Did you try working on derivations of your favourite theories, for example: a derivation of the Schrödinger equation? This can help you gain more insight/understanding into the assumptions that go into an equation. Personally this is the only way for me to study physics on a deep level, and I enjoy it a lot!

I have been thinking about that but I lacked motivation. I guess this is the time to get started! :)
 
  • #14
chiro said:
I think if you can get that kind of understanding in one course, you're either very intelligent, or you have a great teacher or both.

If you can do that, then great. But its just not possible to know all the nooks and crannies and put so many things into context like a professor (or some expert) can. Also don't feel bad about that, because it takes people years and years of their life to get to that stage.

Also since you are saying you are doing a math double major, I think its being a bit hard on yourself to have deep knowledge about math or physics let alone both of them. One thing you should remind yourself is that the stuff you are learning has been done by many dozens (if not hundreds or thousands) of people, all who are very smart, and all who have spent a lot of time to contribute in some small way to the body of knowledge that we take for granted. When you put that into perspective, I think it doesn't make sense to be hard on yourself.

Keep at it, and things will come.

Thank you! After going deeper and deeper into math and physics, I am surprised by how different the ways of thinking in each subject are!
 

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