On Wednesday, May 30, 2018 at 5:55:36 AM UTC-5, [email protected] wrote:
>
> What is the role, if any, of Schrodinger's equation for determining the
> state and evolution of a spin 1/2 particle, written as ( |up> + |dn> ) /
> sqrt (2). I don't see how it's applied. I don't think it's applied. TIA, AG
>
The relativistic Dirac equation is a form of the Schrodinger equation. The
energy momentum interval is m^2 = E^2 - p^2, I have set c = 1, and so
energy is
E = sqrt{p^2 + m^2).
The quantized form of energy is E --> i∂/∂t and the square root has roots
of the form of operators that act on a spinor state
i∂ψ/∂t = α^i∂ψ/∂x^i + mψ
which is a form of the Dirac equation. The square of this must recover the
Klein-Gordon equation and so α^iα_j = δ^i_j. So the Dirac equation is a
form of the Schrodinger equation.
LC
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