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snoopies622

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- TL;DR Summary
- Since the Schrodinger equation incorporates neither spin nor special relativity, why does it describe the hydrogen atom better than the Klein Gordon equation?

my premises:

— one can arrive at the Klein-Gordon equation by applying quantum mechanical operators to the special relativity dynamics equation E^2 = (mc^2)^2 + (pc)^2.

— Schrodinger arrived at this equation, but rejected it because it didn't correctly explain the behavior of an electron in a hydrogen atom.

— the reason it didn't is because it doesn't incorporate spin, so it only works for spin zero particles like the Higgs boson.

— Schrodinger then arrived at his famous "Schrodinger equation" which is based on plugging the deBroglie relation lambda=h/p into a generic wave equation, leaving out special relativity altogether, and he published it because, unlike the Klein-Gordon equation, it does work pretty well with the hydrogen atom.

— Dirac then "took the square root" of the Klein-Gordon equation to produce his Dirac equation, which works even better with the hydrogen atom because it both incorporates particle spin and is consistent with special relativity.

My question is: Since the Schrodinger equation incorporates neither spin nor special relativity, why does it describe the hydrogen atom better than the Klein-Gordon equation?

I realize that my premises probably aren't exactly correct, and would appreciate any feedback.

— one can arrive at the Klein-Gordon equation by applying quantum mechanical operators to the special relativity dynamics equation E^2 = (mc^2)^2 + (pc)^2.

— Schrodinger arrived at this equation, but rejected it because it didn't correctly explain the behavior of an electron in a hydrogen atom.

— the reason it didn't is because it doesn't incorporate spin, so it only works for spin zero particles like the Higgs boson.

— Schrodinger then arrived at his famous "Schrodinger equation" which is based on plugging the deBroglie relation lambda=h/p into a generic wave equation, leaving out special relativity altogether, and he published it because, unlike the Klein-Gordon equation, it does work pretty well with the hydrogen atom.

— Dirac then "took the square root" of the Klein-Gordon equation to produce his Dirac equation, which works even better with the hydrogen atom because it both incorporates particle spin and is consistent with special relativity.

My question is: Since the Schrodinger equation incorporates neither spin nor special relativity, why does it describe the hydrogen atom better than the Klein-Gordon equation?

I realize that my premises probably aren't exactly correct, and would appreciate any feedback.