Dirac Wave Function: Schrodinger Equation Coupling

[jamie.j1989]

Hi, is the wave function that couples to the Dirac equation the same as that which couples to the Schrödinger equation? Thanks.

 

[ddd123]

No, it's different, the biggest difference is that the Dirac equation has a bispinor as a solution. But generally the Dirac wavefunctions follow relativistic transformation rules, the Schroedinger ones are Galileian.

 

[vanhees71]

In addition, it has a completely different physical meaning. It cannot be interpreted easily as a "wave function" like in nonrelativistic physics. The reason is that at relativistic energies, you always can create and destroy particles in scattering processes. The Dirac equations solutions are Dirac-spinor fields. They are best interpreted in their quantized form, leading to relativistic quantum-field theory, because this is the most elegant way to describe particle creation and destruction or, more generally, many-body systems in quantum theory.

 

[ddd123]

Yes. Though I didn't want to stress that because single-particle relativistic QM, inconsistent as it is in the fundamental interactions context, has consequences like Klein's paradox that actually show up in solid state physics iirc.

 

[vanhees71]

Well, the Klein paradox occurs precisely because of the problems when enforcing a single-particle interpretation!

 

[ddd123]

Yes, sorry, I meant things like this: http://arxiv.org/abs/cond-mat/0604323

 

[jamie.j1989]

In addition, it has a completely different physical meaning. It cannot be interpreted easily as a "wave function" like in nonrelativistic physics. The reason is that at relativistic energies, you always can create and destroy particles in scattering processes. The Dirac equations solutions are Dirac-spinor fields. They are best interpreted in their quantized form, leading to relativistic quantum-field theory, because this is the most elegant way to describe particle creation and destruction or, more generally, many-body systems in quantum theory.

I don't quite understand why if particles can be created and destroyed in scattering processes at relativistic energies we can't easily interpret it as a wave function? Also by scattering processes are you referring to particle collisions?

 

[bhobba]

I don't quite understand why if particles can be created and destroyed in scattering processes at relativistic energies we can't easily interpret it as a wave function? Also by scattering processes are you referring to particle collisions?

If particle numbers are not fixed you have a Fock Space and the QFT formalism.

Its inevitable when you combine it with relativity that particle numbers are not fixed - see for example section 8.3 of:
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

Thanks
Bill