Schrodinger tried to interpret the square of the modulus of the wavefunction as the charge density and ran into problems. However, according to Barut, these problems can be overcome.

The following article may be relevant: A.O. Barut, Foundations of Physics Letters, VoL 1, No. 1, 1988, p. 47, _The revival of Schrodinger's Interpretation of Quantum Mechanics_

>Apparently Schrodinger inserted in the nonlinear term in (2) only one term, the ground state wave function of the H atom, instead of the full Fourier expansion, and obtained a too large value of the energy shift. It turns out that this term is only part of the renormalization and not the observable energy shift.