Schrodinger Equation Explained - Get the Answer Now

[Mech-Master]

Hey guys,

I am trying to understand where did this equation exactly come from. I know it is very complex, but anyone can explain it to me in the best way possible?

 

[jtbell]

Do you mean, how did Schrödinger come up with the equation in the first place?

https://www.physicsforums.com/showthread.php?p=418069#post418069

 

[mccoy1]

Do you mean, how did Schrödinger come up with the equation in the first place?

https://www.physicsforums.com/showthread.php?p=418069#post418069

Yes please. I think most people who are trying to learn QM want to ask that question. In most Physics textbooks, it's just mentioned that it can't be proved. But are there any plausible explanations as to how the guy came up wit that equation?

 

[alxm]

Well, of course it can't be proven - this is physics, not pure math.

But IIRC, Schrödinger made some assumptions but basically 'guessed it'. It was first later that it was derived more rigorously from more basic postulates. This is covered in some more advanced QM textbooks (e.g. first chapter of Landau-Lifschitz)

I'm embarrassed I can't remember it all, but you assume a system is described by a wave function, which is continuous, square-integrable and normalized. That the observable properties of the system correspond to eigenvalues of Hermitian operators on that wave function, etc.
(What've I forgotten?)

 

[xepma]

Gaelilean symmetries: spatial and temporal translational invariance, stuff like that. See e.g. the book by Ballentine.

 

[zenith8]

The whole process, including the historical context, is described in Valentini and Bacciagaluppi's recent book, available online here:

http://uk.arxiv.org/abs/quant-ph/0609184"

or on Amazon if you want to buy it.

See section 2.3 p.57 onwards. The relevant bit starts "On 3rd November 1925, Schroedinger wrote to Einstein: 'A few days ago I read with the greatest interest the ingenious thesis of Louis de Broglie...'"