Relativistic vs. non-relativistic quantum mechanics

In summary, for theoretical purposes, one should always use the complete theory to calculate results.
  • #1
Kamper
17
0
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??
 
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  • #2
Than* light*
My iPad's autocorrect, one might question whether the name is fitting, is playing around.
 
  • #3
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.
 
  • #4
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?
 
  • #5
Kamper said:
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?
 
  • #6
George Jones said:
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...;-)
 
  • #7
On*
My apologies
 
  • #8
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.
 
  • #9
So:
Suppose one is examining the hydrogen atom and one is in doubt whether to use the Schrodinger or the Dirac equation. Would one then proceed with the Dirac or, if only the low energy states are of interest, use the Schrodinger?
 

1. What is the difference between relativistic and non-relativistic quantum mechanics?

Relativistic quantum mechanics takes into account the effects of relativity, such as time dilation and length contraction, while non-relativistic quantum mechanics does not. This means that relativistic quantum mechanics is better suited for describing particles moving at high speeds or in strong gravitational fields.

2. How does relativistic quantum mechanics affect the behavior of particles?

Relativistic quantum mechanics predicts that particles moving at high speeds will have a larger range of possible energies and momenta, and may even have negative energies. It also predicts the existence of antimatter and the annihilation of matter and antimatter particles.

3. Can both relativistic and non-relativistic quantum mechanics be applied to all particles?

No, relativistic quantum mechanics is only applicable to particles with non-zero rest mass, while non-relativistic quantum mechanics is used for particles with negligible rest mass, such as photons. Both theories can be applied to particles with zero rest mass, such as electrons, but relativistic effects are only significant at high energies.

4. Is one theory more accurate than the other?

It depends on the situation. Non-relativistic quantum mechanics is accurate for most everyday phenomena, but breaks down at high energies and speeds. Relativistic quantum mechanics is more accurate for describing these extreme conditions, but it is more complex and difficult to solve mathematically.

5. How do the equations differ between relativistic and non-relativistic quantum mechanics?

The equations of relativistic quantum mechanics, such as the Dirac equation, take into account the effects of relativity and have additional terms to account for these effects. Non-relativistic quantum mechanics uses simpler equations, such as the Schrödinger equation, which do not account for relativity.

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