Question

What exactly goes wrong when using the Klein-Gordon equation to calculate the spectrum of hydrogen?

Answer 1

 many textbooks and lecture notes, it says that the Klein-Gordon equation was discarded first because when interpreting it as an equation for a single-particle wave function and trying to calculate the spectrum of the hydrogen atom, it gives wrong results.

But what exactly does go wrong when trying to calculate the spectrum of hydrogen from the Klein-Gordon equation instead of using the Schroedinger equation? How doe the wrong results look like?

Nowhere have I seen a detailled explanation of this issue

Answer 2

In many textbooks and lecture notes, it says that the Klein-Gordon equation was discarded first because when interpreting it as an equation for a single-particle wave function and trying to calculate the spectrum of the hydrogen atom, it gives wrong results.

But what exactly does go wrong when trying to calculate the spectrum of hydrogen from the Klein-Gordon equation instead of using the Schroedinger equation? How doe the wrong results look like?

Nowhere have I seen a detailled explanation of this issue.