Nonrelativistic Quantum Mechanics with Fundamental Environment

Nonrelativistic Quantum Mechanics with Fundamental Environment

“…However, the consideration of a reduced density matrix on a semi-group [20] is quite an ambiguous procedure and, moreover, its technical realization is possible, as a rule, only by using the perturbation method. For investigation of the inseparably linked closed system QSE, a new mathematical scheme has been proposed [5][6][7][8] which allows one to construct all important parameters of the quantum system and environment in a closed form. The main idea of the developed approach is the following.…”

“…A crucially new approach to constructing the quantum mechanics of a closed non-relativistic system QS+FE has been developed recently by the authors of [5][6][7][8], based on the principle of local equivalence of Schrodinger representation. More precisely, it has been assumed that the evolution of a quantum system is such that it may be described by the Schrödinger equation on any small time interval, while the motion as a …”

“…Thus, first of all we need such a generalization of quantum mechanics which includes nonperturbative vacuum as fundamental environment (FE) of a quantum system (QS). As our recent theoretical works have shown [4][5][6][7][8][9], this can be achieved by naturally including the traditional scheme of nonrelativistic quantum mechanics if we define quantum mechanics in the limits of a nonstationary complex stochastic differential equation for a wave function (conditionally named a stochastic Schrödinger equation). Indeed, within the limits of the developed approach it is possible to solve the above-mentioned traditional difficulties of nonrelativistic quantum mechanics and obtain a new complementary criterion which differs from de-Broglie's criterion.…”

On the Dual Concepts of 'Quantum State' and 'Quantum Process'

“…The idea of the excited state of an atom as being actually a system of several atoms answers a need that was identified in Gevorkyan (2012). He pointed to spontaneous transition between quantum levels of a system as a hard-to-explain phenomenon.…”

Quantum Vacuum: The Structure of Empty Space–Time and Quintessence with Gauge Symmetry Group SU(2) ⊗ U(1)

“…where f(t) is a random function, which is clearly defined below (see Eqs. (25) and (26)), and, accordingly, the function ψ ± r, t; f(t) , in this case will mathematically have the sense of a complex probabilistic process (see for example [33,34]), which can be represented as a three-component vector in a Hilbert space:…”