Quantum Theory From a Non-Conventional Perspective

Quantum mechanics is essentially described in terms of complex quantities like wave functions. The interesting point is that phase and amplitude of the complex quantities are not independent of each other, but coupled by some kind of conservation law. This coupling exists in time-independent quantum mechanics as well as in in its time-dependent form. It can be traced back to a reformulation of quantum mechanics in terms of complex nonlinear Riccati equations, where the quadratic term in the latter equation explains the origin of the phase-amplitude coupling. Since realistic physical systems are always in contact with some kind of environment this aspect is also taken into account. It turns out that this dissipative effect can either affect the amplitude or the phase of the complex quantity describing the open quantum system. This suggests a relation between non-unitary transformations and gauge-transformations for these systems. A change of the amplitude also seems to be connected with a second quantum of action for "radial" changes, compared to ħ for "angular" changes, leading to an interpretation of Sommerfeld's constant. (paper)