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Compt. rend.

TRANSFORMATION OF WAVE FUNCTIONS IN A GALILEAN CHANGE OF REFERENCE

C. Budin

Published Oct 31, 1962• 0 citations
OpenAlex

Abstract

The potential of pulse velocities in fluid mechanics was calculated and applied to the transformation of wave functions in functional theory and wave mechanics. (tr-auth)

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It is well-known that Schrodinger wave functions are not covariant under Galilean boosts. To obtain the correct result the boost transformation, t′ = t and ~x′ = ~x − ~vt, must be followed by the phase shift δφ = 12mv 2t + m~v · ~r. A generally accepted approach is to absorb the phase shift into the Galilean boost, construct the Schrodinger group and claim Galilean invariance of the Schrodinger wave function. Here I address the physical meaning of the phase shift. It is not a coordinate transformation since it depends on the mass of the Schrodinger particle. Consequently, one needs as many Schrodinger groups as there are distinct masses. The phase shift does not follow from Lorentz boost per se in the low velocity limit. Covariance of the non-relativistic quantum mechanical kinetic energy and momentum under pure coordinate transformations can be satisfied only by the boost t′ = t ( 1 + 12 v2 c2 + ~v·~r c2 )