SPHERICALLY-SYMMETRICAL SOLUTIONS OF THE SCHRODINGER-NEWTON EQUATIONS

As part of a programme in which quantum state reduction is understood as a gravitational phenomenon, we consider the Schrodinger-Newton equa tions. For a single particle, this is a coupled system consisting of t he Schrodinger equation for the particle moving in its own gravitation al field, where this is generated by its own probability density via t he Poisson equation. Restricting to the spherically-symmetric case, we find numerical evidence for a discrete family of solutions, everywher e regular, and with normalizable wavefunctions. The solutions are labe lled by the non-negative integers, the nth solution having n zeros in the wavefunction. Furthermore, these are the only globally defined sol utions. Analytical supper? is provided for some of the features found numerically.