I've suddenly run into a problem. This has probably arisen from the fact that I've yet to have (and may never have) formal teaching on the relativistic generalisation of QM.

I see the Schrodinger equation proper as

[tex]\hat{H}| \psi (t) \rangle = i\hbar \frac{d}{dt} | \psi (t) \rangle[/tex]

Is this valid in the relativistic case? I guess it must be because wherever I have seen relativistic generalisations, they tend to be relativistic generalisations of the Hamiltonian of the single particle classical Hamiltonian [itex]p^2/2m.[/itex] And as it happens we can recast the above equation into some covariant form (is this coincedence or is it meant to happen?)

But then I later realised that the Dirac equation is more the equation of motion for the spinor field, i.e. in QED, we use the Dirac (for electron spinor field) + EM (for photon field) + interaction (electron-photon) Lagrangian.

In any of this, is the Schrodinger equation proper ever replaced by something else? Or is all we do is find Hamiltonians that describe our relevant particles? And does this apply to particles, or the associated field, or both?

Thanks in advance.

I see the Schrodinger equation proper as

[tex]\hat{H}| \psi (t) \rangle = i\hbar \frac{d}{dt} | \psi (t) \rangle[/tex]

Is this valid in the relativistic case? I guess it must be because wherever I have seen relativistic generalisations, they tend to be relativistic generalisations of the Hamiltonian of the single particle classical Hamiltonian [itex]p^2/2m.[/itex] And as it happens we can recast the above equation into some covariant form (is this coincedence or is it meant to happen?)

But then I later realised that the Dirac equation is more the equation of motion for the spinor field, i.e. in QED, we use the Dirac (for electron spinor field) + EM (for photon field) + interaction (electron-photon) Lagrangian.

In any of this, is the Schrodinger equation proper ever replaced by something else? Or is all we do is find Hamiltonians that describe our relevant particles? And does this apply to particles, or the associated field, or both?

Thanks in advance.

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