In various articles (and books) such as the wiki article of the Klein-Gordon equation wrote:
"The Klein-Gordon equation is a "quantized" version of the relativistic energy-momentum relation";
In the article of "canonical quantization" has been written:
"The Klein-Gordon equation is the classical equation of motion for a free massive scalar field, but also the "quantum" equation for a scalar massive particle wave-function.";
I'd like to know,
What is exact name of the procedure of derivation of Klein-Gordon equation from the energy-momentum relation? (based on the above articles, i.e. by replacing quantities energy and momentum and so on with their corresponding quantum operators)?
Finally, the Klein-Gordon equation is a classical massive field equation, or a quantum mechanical massive wave-function equation, or both?
This question may sound elementary, however, I would appreciate if somebody clearly and simply answer it.