Nonlinear Dynamics and Applications

2006, Vol.13, pp.67-72

The wave equation for a scalar particle in Riemannian space, non-minimal interaction and non-relativistic approximation.
Kisel V.V., Tokarevskaya N.G., Red'kov V.M.

The procedure of the non-relativistic approximation in the theory of scalar particle, charged and neutral, is investigated in the background of Riemannian space-time. A generalized covariant Schrödinger equation is derived when taking into account non-minimal interaction term through scalar curvature R(x), it substantially differs from the conventional generally covariant Schrödinger equation produced when R(x)=0. It is shown that the the non-relativistic wave function is always complex-valued irrespective of the type of relativistic scalar particle, charged or neutral, taken initially. The theory of vector particle proves the same property: even if the wave function of the relativistic particle of spin 1 is taken real, the corresponding wave function in the non-relativistic approximation is complex-valued.
Key words: Wave equation, Riemannian space-time, covariant Schrödinger equation, non-minimal interaction, non-relativistic approximation

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