- #1
nonequilibrium
- 1,439
- 2
Hello,
I'm reading Griffiths' introduction to elementary particles and he seems to claim that the Schrödinger equation can be seen as a non-relativistic limit of the Dirac equation. I was wondering how one could deduce this, e.g. how do we go from
[itex]\mathcal L = \bar{\psi} \left( i \gamma^\mu \partial_\mu - m \right) \psi[/itex]
to
[itex]\mathcal L = \psi^\dagger \left( i \partial_t + \frac{\nabla^2}{2m} \right) \psi[/itex]
(and somewhere along the way the psi goes from having 4 components to having one (?))
But maybe I misinterpreted Griffiths; he simply states that the psi of the Dirac equation non-relativistically becomes the regular quantum mechanical wavefunction, and I assumed the latter to be the psi of the Schrödinger equation.
I'm reading Griffiths' introduction to elementary particles and he seems to claim that the Schrödinger equation can be seen as a non-relativistic limit of the Dirac equation. I was wondering how one could deduce this, e.g. how do we go from
[itex]\mathcal L = \bar{\psi} \left( i \gamma^\mu \partial_\mu - m \right) \psi[/itex]
to
[itex]\mathcal L = \psi^\dagger \left( i \partial_t + \frac{\nabla^2}{2m} \right) \psi[/itex]
(and somewhere along the way the psi goes from having 4 components to having one (?))
But maybe I misinterpreted Griffiths; he simply states that the psi of the Dirac equation non-relativistically becomes the regular quantum mechanical wavefunction, and I assumed the latter to be the psi of the Schrödinger equation.