# The History and Development of Schrodinger's Wave Equation

1. Feb 5, 2004

### Entropia

"The History and Development of Schrodinger's Wave Equation"

i am taking a class in "the history of chemistry" and i chose to write a paper on "the history and development of schrodinger's wave equation"...

does anybody have any suggestions on what kind of topics i should include?

2. Feb 5, 2004

### lethe

Re: "The History and Development of Schrodinger's Wave Equation"

well, definitely include Einsteins idea about the quantum nature of light ($E=h\nu$)

from there, deBroglies hypothesis that the same thing may apply to matter

from there, it was an easy step for Schr&ouml;dinger (who was one of the foremost experts on wave mechanics) to turn this hypothesis into a wave equation.

it is worth mentioning that Schr&ouml;dinger first wrote down what we now call the Klein-Gordon equation, which is a relativistic wave equation, but abandoned this approach, because it seemed to lead to negative energy solutions, which lead to instabilities of the theory. so he turned to the nonrelativistic version, what we call Schr&ouml;dinger's equation today.

also worth mentioning is how, while Schr&ouml;dinger was doing all this, Heisenberg and Born were developing matrix mechanics, a completely different approach to quantum mechanics. for a little while, the entire field was split into two camps, the matrix mechanics people and the wave mechanics people, and they would make insults about each others theories. at the time, people thought one theory must be wrong, and only one would survive.

another thing worth mentioning is that the variation method of approximation in quantum mechanics was formulated in Schr&ouml;dinger's wave mechanics, and it was the first successful quantum treatment of a multi-electron atom. Bohr's theory (quantize the action) was completely unsuccessful for Helium, and no one knew how to use Heisenberg's and Born's matrix mechanics on the hydrogen atom (perturbation theory doesn't work so well), so this was a great success for wave mechanics, and convinced a lot of people that it was correct. for this reason, the chemist will almost exclusively work with Schr&ouml;dinger's wave mechanics, and never with Heisenberg's matrix mechanics.

then Schr&ouml;dinger derived an equivalence between matrix mechanics and wave mechanics. von Neumann and others made this into a rigorous proof, known as the Stone-von Neumann theorem, and ever after, any physicist has felt free to use whichever is more convenient for the problem at hand. for us, they are not two different theories, but rather two different ways of writing the same theory, Quantum Mechanics.

in fact, today, we use Dirac's bra-ket notation, which can be used for either wave mechanics or matrix mechanics (these days, the fact that they are the same is obvious to anyone. the only difference between the approaches is whether the time dependence lives in the operators or the states, and you change from one to the other by multiplying by $e^{iHt}$)