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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.

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# The Schrödinger equation as the non-relativistic limit of the Dirac equation

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