- #1

ginda770

- 9

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In multiple textbooks I've seen it said that a single particle wave function (no spin) transforms as a Lorentz scalar. I.e. if we have a Lorentz transformation from an old frame to a new frame

[tex]\overline{x}=\Lambda x[/tex]

(x is short for (t,x,y,z)) then the wave function in the new frame and the old frame are related by

[tex]\overline{\psi}(\overline{x})=\psi (x)[/tex]

My question is this: The square of the wave function is a probability density, so why doesn't it transform as the zeroth (time) component of a 4-vector as other densities do?