Why Does Quantum Mechanics Feel So Incomprehensible?

[Just a nobody]

I've taken an intro QM course (1-dimensional systems and hydrogen atom) and I'm currently 3 weeks into the second undergrad QM course. We went over angular momentum and the professor is covering spin right now.

In terms of grades, I'm doing okay: I received a 3.5 in the intro course and I'm getting acceptable grades on the homework so far in my current course. However, I don't feel like I understand the topic at all. It feels more like a sea of eigenfunctions and operators than a coherent description of the world. All of the problems I've been given seem completely artificial: find some normalization constant, calculate the value of some operator acting on something, derive equation x from equation y. (Edit: book is Introduction to Quantum Mechanics by Griffiths)

While taking classical mechanics and statistical mechanics, I felt like I was developing a good intuition of how things work, but with quantum mechanics I'm still completely lost. Is there anything I can do to understand things a little better?

 

[kote]

Unfortunately, one of the things about QM is that it doesn't make any sense intuitively :). That's the only thing there really is to "get" - that you can't visualize it. What's really astounding about QM is that, assuming it's valid, it proves that the world is not made up of particles and forces that can be understood in 3 dimensions.

It probably will help you very little with your grades, but if you want to understand it, I actually recommend reading Niels Bohr's "Atomic Theory and the Description of Nature" - https://www.amazon.com/dp/0918024501/?tag=pfamazon01-20. Bohr talks a lot in there about the "visualizability" of QM (or rather, the lack thereof). It's very readable, and Bohr's actual thoughts are almost nothing like what you read today about the "Copenhagen Interpretation."

If that really interests you, you may even want to see if there is a decent philosophy of physics course offered at your school.

 

[eri]

I took that class as a junior (from Griffiths himself, who was a great teacher) and I really didn't get it. Managed to pull off a B- in the class somehow, but really didn't feel confident about it. However, around the second semester of it, the work started making more sense, and about my 4th class (while working on the PhD) I was doing fine. Sometimes it just takes a while to click. Don't slack off - but don't think this means you can't do physics either.

 

[DDTea]

I remember when I took an intro QM class (the first time, and I failed). Our professor was hilarious. He liked to write quotes on the board and some that I remember were:

"You cannot hope to understand quantum mechanics; you can only get used to it."
"Shut up and calculate!"
"Don't panic" (in regard to Hermite polynomials)

Anyhow, it's a field where it's easy to lose the forest for the trees. I strongly recommend Richard Feynman - QED. He explains how quantum mechanical calculations are done and what they mean without using a single equation. It's a very quick read too. Read the introduction to it as well.

 

[ParticleGrl]

All of the problems I've been given seem completely artificial: find some normalization constant, calculate the value of some operator acting on something, derive equation x from equation y. (Edit: book is Introduction to Quantum Mechanics by Griffiths)

Unfortunately, the hydrogen atom is one of the only exactly solvable problems, physically realistic problem you'll ever run into quantum mechanics. This means that intro courses are peppered with mathematical exercises and infinite square well problems that seem not only weird because of quantum mechanics, but also extremely contrived. Thats because they are.

It will get worse before it gets better- quantum mechanics matches the hydrogen atom extremely well, and so it will become your training ground. You'll learn how to find approximate solutions and perturbative solutions by investigating the spectrum of the hydrogen atom in painstaking detail, etc. You have to slog through all this math and all this build up to even begin to consider the really interesting stuff.

This is because, unfortunately, no one has come up with a really interesting set of great introductory quantum mechanics problems. However, more approaches are always good. Try reading the first few chapters of this: http://people.ccmr.cornell.edu/~mermin/qcomp/CS483.html Its very readable, and comes at quantum mechanics from a completely different angle. Its far more abstract, but if you like computation theory, its fantastic.

While taking classical mechanics and statistical mechanics, I felt like I was developing a good intuition of how things work, but with quantum mechanics I'm still completely lost. Is there anything I can do to understand things a little better?

One thing to do may be to grab a book with a good introduction to the path integral. While standard quantum mechanics is formulated in the strange land of phase space, the path integral is formulated in the 4d world we live in. I find this helps to build intuition. Unfortunately, its useless for doing most of the calculations you need for an intro class (although fantastic for some problems you may encounter later in life). Shankar has a good introduction. If you are already familiar with lagrangian mechanics, it will be a bonus.

 

[MathematicalPhysicist]

Nobody gets QM. (pun intended).

 

[kote]

Nobody gets QM. (pun intended).

I don't get it.

 

[kote]

...sorry

 

[jeebs]

i know the feeling, and it just eases with the more QM you study, the more problems you solve, the more you try and get into the mindset. I wouldn't say I have a deep understanding of it but with practice you become more "fluent" in it (I'm speaking as a student here too, I was probably asking the same question 18-24 months ago).

 

[Shackleford]

I don't get it.

Feynman.

 

[G01]

No one really gets quantum mechanics, however, everything starts becoming more coherent the more you study it.

I felt the same as you do when I was an undergrad. QM seemed to be bits and pieces of math stuck together randomly. Eigenfunctions here, operator algebra there, differential equation in between. However, once I started studying it in my first year grad quantum class, I realized the theory does indeed follow from a set of first principles and axioms, just like classical mechanics does.

Hang in there!

 

[Shackleford]

No one really gets quantum mechanics, however, everything starts becoming more coherent the more you study it.

I felt the same as you do when I was an undergrad. QM seemed to be bits and pieces of math stuck together randomly. Eigenfunctions here, operator algebra there, differential equation in between. However, once I started studying it in my first year grad quantum class, I realized the theory is indeed a contingent whole. Hang in there!

Did it become quite a bit more difficult in grad school?

 

[G01]

Did it become quite a bit more difficult in grad school?

The workload was greater, and yes, the problems were longer and more difficult, and involved tougher math. However, with the increase in difficulty of problems comes a better understanding of the theory. (This is why we solve problems in physics classes, right?)

I'm not saying I intuitively understand QM(like we said, no one really does), but now, I do get that the theory is more coherent than I thought it was as an undergrad.

 

[jtbell]

I didn't really "get" a lot of what I saw in my undergraduate QM course, even after going through grad school, until I had to teach an undergraduate QM course myself. Third time around was the charm for me.

 

[nlsherrill]

I didn't really "get" a lot of what I saw in my undergraduate QM course, even after going through grad school, until I had to teach an undergraduate QM course myself. Third time around was the charm for me.

lol the third time teaching it you finally got a good grasp, or just third class you took on it? Jesus how difficult is QM??!

 

[clope023]

Noone is supposed to be able to relate to the point of view of a subatomic particle, I'm guessing this is where the difficulty stems from.

 

[dark_raider]

Quoting Feynman: "i think i can safely say that nobody understands quantum mechanics."

 

[G01]

lol the third time teaching it you finally got a good grasp, or just third class you took on it? Jesus how difficult is QM??!

This is really the way it is with most things, when you think about it. You never truly understand something until you're able to effectively explain it to someone else.

In that sense, I think helping out here on PF in the Homework forums has really helped my understanding of physics.

 

[alemsalem]

It's really frustrating that you can't visualize QM, in classical physics it feels easy to recognize what the equation is trying to say and what is going on, you might even be able to predict just by running it in your head the nature of the result. but even in classical mechanics it might not be so clear and what makes the prediction is an equation and its interpretation.

the way I imagine what (theoretical) physicists are trying to do is that they are trying to create patterns on papers (or computers) through mathematics that after proper interpretation gives us what we see in reality, its like we are trying to understand a foreign language. and little balls running around each other or something else we are used to is just not that language, on the other hand eigenvalues and eigenstates are parts of the language we create to get what we observe.

(I'm not an expert, it's just a rough view)

 

[Simfish]

Try the Falstad math/physics applets:
http://www.falstad.com/mathphysics.html

There are also "Visual Quantum Mechanics" books you can check out.

 

[dark_raider]

Understanding QM needs a serious amound of time. Ok, you're going to be able to handle the exercises of the books you study from, hopefully from the beginning. But if you want a deep understanding of quantum theory, well, that's a different story.