Visual Quantum Physics | Hacker News Reader

Visual Quantum Physics

visualquantumphysics.org

134 pointsbindidwodtj19 comments

If this is your thing, you'll enjoy my wavefunction visualizer:

You can drag around the potential, energy levels, etc. and it will do its best to solve the 1D time-independent Schrödinger equation (Numerov method). Turn the dial to see it in 3d, with imaginary components in the z direction. Momentum-space solution can also be enabled.

Built on WebGL and TypeScript, source is at https://github.com/ridiculousfish/wavefiz

Thanks for sharing!

I have a tangential question.

I'd love to be able to get into stuff like this, but when I see the pages of equations.... my eyes just glaze over and I lose track of what's what.

I get that it's a skill I lack and I'd love to improve on it. I'm wondering if anyone knows any good resources specifically for this? Something that takes you through _how_ to read equations, preferably something that starts off simple and gradually gets more complex?

Intuitively I can watch something like a 3Blue1Brown video and get it (or at least feel like I understand it on some level). I'm just not sure where to find practice material for reading equations that doesn't start right at the deep end, or even if I'm looking at this in the correct way.

For reference I have no trouble jumping into a new programming language; I immerse myself in the culture and idioms of the language, learn what the reasoning behind the design of the language is, learn the syntax, etc. I just can't seem to find a way to do this with written math and equations.

My two cents (as someone a bit more familiar with this stuff):

I don't think there is a single universal skill at play. Much like reading code, I think it depends on your familiarity with the specific 'programming language' in which the code/argument is written: show, say, Lisp to a Javascript-only programmer, and they would likely get stuck as well.

In this particular case, I happen to be familiar with this particular dialect of mathematical physics (and its style of argumentation), so I was able to follow along. But show me, say, some crazy algebraic number theory stuff, and I would be totally lost.

Going back to your question, then, I suggest getting familiar with the particular mathematical 'dialect' (and, I cannot emphasize more, style of argumentation) you are interested in.

For example, in this particular case, I would read up on --and, ideally, develop some 'muscle memory' for-- (some) differential equations and multivariate differential calculus using, say, Khan Academy.

(A bit of familiarity with the somewhat non-constructive style of argument of 'modern' classical mechanics wouldn't hurt either.)

Thanks for these pointers.

If you're interested in getting more intuition for quantum mechanics, I recommend starting with discrete systems (e.g. qubits) rather than continuous ones. The latter approach is how QM was discovered, mostly, and still unfortunately dominates the educational material, but an introductory focus on qubit is becoming more popular in light of the success of quantum information as a field. Almost all the deep and confusing parts of QM can be learned with qubits, and it's much easier to do so without adding continuum complications.

Scott Aaronson has a good point of view that one of the better ways to teach QM is as probability theory generalized to complex numbers. I learned it the old-fashioned physics way, but I have more of a programming mindset, so it probably would have made more sense starting from the quantum information approach.

I think the real mind-blowing thing is that most of quantum computing can be described as applying a unitary matrix operation to some state vector and computing the result. The rest of the field is just about what those unitary operations are and how you chain them together. (Oh... and the whole engineering problem of actually building a machine that does that without decoherence)

Some pointer would be helpful to those of us found the field very hard to follow

Google return one of this and I link to the all chapter one:

http://www.damtp.cam.ac.uk//user/eal40/teach/QM2012/allchapt...

Any good?

well, in that sense the op was saying disregard the real factors of complex numbers, use only 1 and i.

In sum, I interpret that as a start from binary probability. The bayesian rule for example follows trivially from Laplacian equal-chance decision trees, so I think that's a good hint. Does the bayesian/frequentist distinction play a role here (I'd like to think it's not a fundamental distinction, but I really don't know).

> well, in that sense the op was saying disregard the real factors of complex numbers, use only 1 and i.

This is incorrect. The quantum mechanics of discrete systems still requires the use of the continuous field of complex numbers for the amplitudes of different configurations (not just the fourth roots of unity or anything like that). The "discrete" refers to the discreteness of the configuration space (e.g., the discrete spin of an electron, in contrast to the continuous position x of a particle).

Very analogously, one can do classical probability theory for discrete (e.g., binary) outcomes or continuous ones, but either way you need to use the continuous interval between 0 and 1 to represent probabilities for those outcomes. Restricting to binary probabilities (i.e., true or false) would be classical logic, a subset of probability theory.

(It's possible to work with an equivalent formulation of quantum mechanics with only real numbers, rather than complex amplitudes, but these numbers must still be continuous and allowed to go negative. The Wigner representation is an example.)

Incidentally, mixing up the continuity of the amplitude with the continuity of configurations is exactly the sort of mistake it's easy to make when these things are introduced simultaneously! So your misconception is exceedingly reasonable.

Any good resources you can recommend?

I am still a big fan of this book.

https://www.amazon.com/Quantum-Computation-Information-10th-...

It exists also as a digital version.

Agreed, it's still excellent. Obviously it doesn't contain the many new results that have appeared since it's final edition, but that's irrelevant for the learning the basic information-theoretic aspects of quantum mechanics.

"Materials" section from my "Quantum mechanics for high-school students": https://p.migdal.pl/2016/08/15/quantum-mechanics-for-high-sc...

As a fair warning - Bohm interpretation (even though as fine as any other interpretation of quantum mechanics), is neither the most popular or the easist to follow (don't be tempted).

(If you already know QM (as in: are able to perform calculations in QM, rather than "listened/read to however many hours of narration"), disregard this warning.)

In general, I strongly advise against starting from classical mechanics to understand quantum mechanics. While is the classical, and historic, way - it gives a lot of paradoxes and confusion.

Just start with a two-state system (ideally polarization of light, but spin-1/2, while harder and less intuitive, is still OK). Then only well after that (including 2-3 particles, entanglement, etc), and provided you learn Fourier transformation beforehand, move to position & momentum stuff.

See http://p.migdal.pl/2016/08/15/quantum-mechanics-for-high-sch... for my longer overview from my experience of teaching quantum mechanics to high-school students (and I link to the books & sources I find the best). And of course the Quantum Game with Photons: http://quantumgame.io/

If you want to skip to the more visual stuff, see the gallery of videos:

http://www.visualquantumphysics.org/?page_id=397

This one, in particular, I find amazing:

https://www.youtube.com/watch?v=HHSluoPqank

(Even if you have studied this stuff before, 'seeing' the solutions in this way is pretty cool IMO.)

In case somebody wonders, apparently most (if not all) photos and videos are made with Mathematica.

I think that website has been there for quite a time. You can also tell from the technical standard (embedding LaTeX equations as pictures, low-res plots, etc.). Nevertheless plotting in physics is crucial! :)

Is there a reason to refuse to explicitly label variables, especially in a pop-sciesque article like this?

I could more or less follow the math but because I havent memorized a dictionary of Greek variable meanings this becomes meaningless.

What's the point? You're alienating everyone but the people who already know exactly what you're talking about and you're left preaching to the choir.

It's unfortunate because this seems really interesting.

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