#### Bulg. J. Phys. vol.33 no.3 (2006), pp. 217-229

#### Quantum Mechanics on a Noncommutative Geometry

T.P. Singh

go back^{}*Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India*Abstract.Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such classical matter fields, quantum mechanics should be formulated without reference to a classical time. If such a new formulation exists, it follows as a consequence that standard linear quantum mechanics is a limiting case of an underlying non-linear quantum theory. A possible approach to the new formulation is through the use of noncommuting spacetime coordinates in noncommutative differential geometry. Here, the non-linear theory is described by a non-linear Schrodinger equation which belongs to the Doebner-Goldin class of equations, discovered some years ago.