Physics
Scientific paper
Oct 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006apei...13..449v&link_type=abstract
Apeiron, vol. 13, numb. 4, p. 449-454
Physics
4
Schroedinger, Galilei Covariance, Galilei Boost
Scientific paper
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 delta Phi=mv^2t/2+mv.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+v^2/(2c^2)+v.r/c^2) and x' = x-vt. hus proper time and relativity of simultaneity are seen to be the roots of non-relativistic quantum mechanical inertia.
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