Relativistic vs. non-relativistic quantum mechanics

[Kamper]

Would one consequently use relativistic QM or in some cases use the non relativistic postulates when dealing with a problem in the same that classical physics are used frequently when one deals with objects traveling at speeds much lower then the speed of ligth??

 

[Kamper]

Than* light*
My iPad's autocorrect, one might question whether the name is fitting, is playing around.

 

[kevinferreira]

One fairly uses non-rel. QM when dealing with low energy systems. The only systematic and meaningful way of using relativistic QM is through quantum field theory, when one has to deal with the possible creation/annihilation of particle species.

 

[Kamper]

But is a general inadequacy in the theory to blame for the limited use or does it just speak to the practical nature of physicsist?

And wouldn't one risk missing important points if one's system evaluation is non relativistic?

 

[George Jones]

But is a general inadequacy in the theory to blame for the limited use or does it just speak to the practical nature of physicsist?

And wouldn't one risk missing important points if one's system evaluation is non relativistic?

If you drop your keys, do you use general relativity to calculate how long it takes your keys to hit the ground?

 

[Kamper]

If you drop your keys, do you use general relativity to calculate how long it takes your keys to hit the ground?

Well, depends ón how meticulous you are...;-)

 

[Kamper]

On*
My apologies

 

[kevinferreira]

All risk is of course calculated.
Even with gravitation, for pratical issues Newton's law is fairly used because it is a very good approximation, and a 5cm error when computing the position of the moon is not a big deal.
The thing is, when dealing with a problem one has to evaluate in what regime the problem undergoes. Sometimes the system always stays in a classical regime and it is a very good approximation to use non-relativistic results.
Of course when in doubt use the complete theory and then proceed to evaluate the contribution of relativistic corrections to see of their importance.
For theoretical purposes, always use the complete theory, and then compute in different regimes if necessary. I would say this is a kind of 'common sense' aproach.

 

[Kamper]

So:
Suppose one is examining the hydrogen atom and one is in doubt whether to use the Schrödinger or the Dirac equation. Would one then proceed with the Dirac or, if only the low energy states are of interest, use the Schrödinger?