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Symmetry classification of two-body central potentials in a two-particleSchr\"{o}dinger equation in terms of contact transformations of the equationhas been investigated. Explicit calculation has shown that they are of the samefour different classes as for the point transformations. Thus in this problemcontact transformations are not essentially different from pointtransformations. We have also obtained the detailed algebraic structures of thecorresponding Lie algebras and the functional bases of invariants for thetransformation groups in all the four classes

Contact Symmetry of Time-Dependent Schrödinger Equation for a Two-Particle System: Symmetry Classification of Two-Body Central Potentials