Schrodinger's Equation: Reason for Acceptance?

[captain]

can anyone tell me the reason why they came to accept this equation with no mathematical proof behind it/ was ther any experiment that supported this equation so that it held true?

 

[Meir Achuz]

It gave the correct properties of hydrogen.
It gives correct results for thousands of other experiments.

 

[G01]

Shrodinger's Equation is analogous to Newton's Second Law in classical physics.

There is no derivation of Newton's Second Law. It is based completely off our observations and experiments showing, directly or indirectly, that F=ma. The same is true for the Shrodinger Equation. Once we observed that matter had wave properties, the Shrodinger Equation was devised to describe those properties. The equation is accepted because experiments have shown that it, (or more generally, it's relativistic counterpart) it makes very accurate predictions. This is how physics works. The ultimate proof is not mathematical, but natural. You can have an amazing derivation for a given equation, but if it doesn't agree with nature, it is not physics.

 

[captain]

i know that the time independent equation gives the eigenvalues and eigenstates for the energy, but what does the time dependent equation help you with (or does that violate the Schrödinger picture of quantum mechanics)?

 

[Meir Achuz]

Scattering and decay are described by the time dependent equation.
Your questions are 80 years late.

 

[premagg]

1)Heisenberg's uncertainity principle
2)Hydrogen atom spectrum
3)electron density in hydrogen atom
4)Properties of hydrogenic atoms.
5)Electromagnetic theory
6)Photoelectric effect
7)Electron diffraction
and the list is endless

 

[captain]

i just want to confirm the fact that Schrödinger's equation didn't include magnetism because it could only be described by tensors

 

[olgranpappy]

i just want to confirm the fact that Schrödinger's equation didn't include magnetism because it could only be described by tensors

It's trivial to include an external magnetic field in Schrödinger's equation--just use minimal coupling... Schrödinger's equation is certainly valid in the presence of electromagnetic fields.

 

[jtbell]

Schrödinger's equation doesn't include any specific kind of force explicitly. Forces come in by way of the potential energy function that is part of the SE. Any interaction that can be described in terms of a potential energy function can be used in the SE.

In general, the magnetic force is not conservative so there is no potential energy associated with it. However, the orientation of a magnetic dipole in a magnetic field does have a potential energy associated with it. By inserting this into the SE you can explain the Zeeman effect, for example (splitting of spectal lines in a magnetic field).