Talk:Schrödinger equation

Umlaut

Anyone know how to type the O with a colon over it in Schrodinger...?

I do not know, but you can always copy-paste. --Alex Halicz (hello) 11:43, 8 February 2007 (CST)

Easy when you are on a MAC, cut and paste when you do not have easy access. Robert Tito | Talk 11:44, 8 February 2007 (CST)

concepts in quantum theory

Can I suggest some discussion of its physical implications (eg quantized energy levels in atoms) in addition to the math. The first mention in The Feynman lectures on Physics, Volume III, Feynman's red book is a good model Cheers David Tribe 15:55, 12 February 2007 (CST) David, would you mind sticking to biology? (Attention: David has a big nose.) Robert Tito | Talk 16:53, 12 February 2007 (CST)

Your dutch phraseology RT has deterred me enuf to make sure I leave the article itself alone. So I now hesitate before leaving this as a possible link

• Why Quantum Mechanics Is Not So Weird after All PAUL QUINCEY. Richard Feynman's "least-action" approach to quantum physics in effect shows that it is just classical physics constrained by a simple mechanism. When the complicated mathematics is left aside, valuable insights are gained. David Tribe 19:18, 12 February 2007 (CST)

Good idea; I'll get right on that. Thanks for the link. Michael Evans

And IMHO the most important missing information (at least for a non-physicist who doesn't even try to understand the equations) is: Does this equation have something to do with the observability properties of quantum states (aka "Schrödingers Cat")?

--Markus Baumeister 15:10, 20 February 2007 (CST)

cat

since quantum mechanics is about statistical chances and wave functions being their advocates, the S.Eq. is the mathematical description of these chances. As such the S.Eq. is a statistical equation (at least when solved) and yes: S's cat is about the chance you will find the cat alive after x days with each previous day a chance of X% to get a lethal piece of food. It also is linked to the quantum inflation induced creation of a pair of electron/positron. Both travelling as wave through cosmos. Upon the moment one observer determines the charge of ONE of these electrons the charge of the other particle is immediately known. (instant communication without loss of time). Remember before measuring you don't know what the particle is. Observation determines sometimes the outcome. Robert Tito | Talk 15:16, 20 February 2007 (CST)

3D Schrödinger in Cartesian coordinates, and other coordinates?

Is the plan to give the Q.E. in 3D-cartesian, cilinder, polar coordinate? Robert Tito | Talk 01:31, 18 February 2007 (CST)

I can do that; I'll probably just put the cylindrical and spherical versions underneath the 3-d Cartesian (which is already there, see the eqn. with the Laplacian?). Michael Evans

Why not put the laplacian in (I guess more known goniometric form (sin/cos, i) )? Besides the idea of an operator somehow comes out of the blue (where it follows 19th centurian hamiltonian physics). Just a few thoughts. Robert Tito | Talk 14:06, 18 February 2007 (CST)

Robert--I think you're confusing the Laplacian (which is simply the three-dimensional total derivative) with Euler's formula, exp(i*theta) = cos theta + i sin theta. Michael Evans No, the way it is now is exactly as I intended/meant. I only miss the cilindrical version.

One other thing - referring to the schrödinger's cat - is the philosophical implications. (god dont play dice etc.) I miss somehow the emphasize on the difference to the classical solutions - where the classical is just the S.Eq. applied on these situations. For the lay it might be interesting to solve the S.Eq. for a H-atom and a billiard ball. Stressing features such as weight, broglie, potential. It might be an eye-opener that quantum is not strange but a more precise determination of what the world is. It might be something that can be copied or used in other parts of physics - but then why not, it can belong here as well. Robert Tito | Talk 00:29, 21 February 2007 (CST)

The reference to WP seems circular Robert Tito | Talk 00:42, 21 February 2007 (CST)

If I may sound a dissenting note; it's not clear to me why the equation in spherical coordinates is added. It does not seem to add anything (unless the plan is to solve it, for example in connection with a discussion of the hydrogen atom).

I find the motivation rather weak. Where does the assumption that ψ is this complex exponential come from? If this is all the motivation that the article is going to contain, then perhaps you should consider deleting it. Just posit the equation, say that its solution in a zero potential is exp(...), and that this corresponds with constant probability.

It should probably explained how to reconcile the section "Discrete Energy Levels" with the fact that the Laplacian (the only example for H given) has a continuous spectrum.

Sorry to be so critical, but it is easier to criticize somebody else's writing than to write something yourself! Cheers, Jitse Niesen 06:26, 21 February 2007 (CST)

audience

while writing an article about the SE and its history and implications an important thing to be aware of is the audience: who is reading this? Very likely it is interested persons, most likely without a solid maths background. They have knowledge about goniometry, but operators and laplace might very easily be too much to ask. That is one of the reasons I like the written out version of the Laplace because sin and cos are known territories. In concordance to David Tribe's remark it may be nice to show QM is just classical mechanics with a twist, BUT the differences lead to very different interpretations - and these are very interesting. Robert Tito | Talk 13:34, 21 February 2007 (CST)

That's what the link to the "Laplacian" article is for. Learning the Laplacian only in the context of quantum mechanics might end up giving someone the wrong idea. The "Laplacian" article should be the place for a description of the Laplacian, don't you think?--Michael Evans 01:26, 24 February 2007 (CST) yup, I agree, it does however also allow us to go in depth on the S.E page (once it has been shortly outlined. Robert Tito | Talk