Paper detail

Complexified quantum and classical mechanics

The anti self-adjoint operators of coordinate and momentum are introduced and applied in discussion of tunneling through the potential barrier where imaginary value of momentum unavoidably appears. Tunneling through temporal barrier is proceeded in a similar way and it is shown that the quantum system can tunnel, while the classical systems are destroyed by such barrier. The imaginary observables of coordinate and momentum are used in a novel treatment of passage through the event horizon. By considering the event horizon as the border of the finite potential barrier, it is found that there is no singularity at the center of a black hole. The imaginary variables of coordinate and momentum are used for the construction of a toy model of the universe. It is shown that the acceleration of the expansion of the universe does not need dark energies to be explained since negative energies are present and characteristic for the imaginary world.