  It is shown that Schroedinger equation is not consistent with information
theory. From the modified form of information which ensures that the most
probable density function it yields tallies with a general form of continuous
Riemann integrable density function that has real or imaginary zeros or
singularities at end points of $[a,b] \epsilon R$, a new variational
formulation for quantum mechanics is proposed that yields a system of
Euler-Lagrange equations that are non-linear. It is proved that the solutions
of this system are unique, orthonormal and complete. One dimensional harmonic
oscillator has been solved.
