A QUANTUM POTENTIAL APPROACH FOR THE GRAVITATIONAL SCHRÖDINGER EQUATION AND ITS REDUCTION INTO THE LANE–EMDEN EQUATION OF INDEX 2

It is shown that the eigenvalue equation in the Jones' treatment of gravitational self-energy may be obtained from a model of extended particles using the quantum potential in the causal interpretation of quantum mechanics and reduced to the Lane–Emden equation of index 2 that has been discussed extensively in the theory of stellar evolution.