
Visual Quantum Physics - bindidwodtj
http://www.visualquantumphysics.org/
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ridiculous_fish
If this is your thing, you'll enjoy my wavefunction visualizer:

[http://ridiculousfish.com/wavefiz/](http://ridiculousfish.com/wavefiz/)

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](https://github.com/ridiculousfish/wavefiz)

~~~
tehsauce
Thanks for sharing!

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Fr0styMatt88
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.

~~~
gone35
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.)

~~~
Fr0styMatt88
Thanks for these pointers.

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jessriedel
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.

~~~
Xcelerate
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)

~~~
posterboy
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).

~~~
jessriedel
> 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.

------
stared
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...](http://p.migdal.pl/2016/08/15/quantum-mechanics-for-high-school-
students.html) 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/](http://quantumgame.io/)

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gone35
If you want to skip to the more visual stuff, see the gallery of videos:

[http://www.visualquantumphysics.org/?page_id=397](http://www.visualquantumphysics.org/?page_id=397)

This one, in particular, I find amazing:

[https://www.youtube.com/watch?v=HHSluoPqank](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.)

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ktpsns
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! :)

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anm89
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.

