Possible confinement mechanisms for nonrelativistic particles on a line

The gauge model of nonrelativistic particles on a line interacting with non standard gravitational fields(5) is supplemented by the addition of a (non) -Abelian gauge interaction. Solving for the gauge fields we obtain equation s, in closed form, for a classical two-particle system. The corresponding S chrodinger equation, obtained by the Moyal quantization procedure, is solve d analytically. Its solutions exhibit two different confinement mechanisms- dependent on the sign of the coupling lambda to the nonstandard gravitation al fields. For lambda > 0 confinement is due to a rising potential, whereas for lambda < 0 it is due to the dynamical (geometric) bag formation. Numer ical results for the corresponding energy spectra are given. For a particul ar relation between two coupling constants, the model fits into the scheme of supersymmetrical quantum mechanics.