DISCUSSION OF THE CENTER OF MASS MOTION IN A SYSTEM WITH THREE DEGREES OF FREEDOM

Abstract

This paper considers the problem of the center of mass motion of three fermionic particles, e. g., equal nucleons (no spin), which can move only in the x-direction in the laboratory system. This system (with three degrees of freedom only) is transformed to a system where one coordinate is proportional to the center of mass coordinate. The center of mass moves in a harmonic oscillator potential. The basis set of wave functions is constructed with Hermite polynomials in part. As example we study the case of a quadratic intrinsic potential between the particles. The problem may be important for the motion of three nucleons in a crystal channel.