  A modified lagrangian with causal and retrocausal momenta was used to derive
a first causal wave equation and a second retrocausal wave equation using the
principle of least action. The retrocausal wave function obtained through this
method was found to be equivalent to the complex conjugate of the causal wave
function, thus leading to the conclusion that a retrocausal effect is already
implicit in quantum mechanics through the means of complex conjugation of the
wave function when computing the probability density for a particle. Lastly,
the same variational principle was employed with a fractionary langriangian,
(that is, containing fractional Riemann derivatives) to obtain a pair of
modified wave equations, one causal and other retrocausal, both of which
correspond to the differential equation of a damped oscillator in the free
particle (potential energy V=0) case. The solutions of this damped wave
equations remain to be explored.
