On the Unitarity of the Quantum Telegraph Equation and Measurement as Bayesian Update from Maximum Entropy Prior Distribution

The quantum telegraph equation is solved for unitary solutions, which links the eigenvalues of the Hamiltonian directly to the oscillation frequency. As it has been showed previously that this PDE is the formal square of a Dirac operator, and on the other hand it is a linearized Hamilton-Jacobi-Bellman PDE, from which the Schrödinger equation can be deduced in a nonrelativistic limit, it is clear that it is the key equation in relativistic quantum mechanics. We give a stationary solution for the quantum telegraph equation and a Bayesian interpretation for the measurement. The stationary solution is understood as a maximum entropy prior distribution and measurement is understood as Bayesian update.