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Classical and quantum mechanics for an extended Heisenberg algebra with canonical commutation relations for position and momentum coordinates are considered. In this approach additional noncommutativity is removed from the algebra by linear…
We propose a new quantum approach for describing a system of $n$ interacting particles with variable mass connected by an unknown field with variable form ($n$-VMVF systems). Instead of assuming any particular nature for variation of the…
It is shown that under certain conditions the resonant transport in mesoscopic systems can be described by modified (quantum) rate equations, which resemble the optical Bloch equations with some additional terms. Detailed microscopic…
We have revealed three fatal errors incurred from a blind transferring of quantum field methods into the quantum mechanics. This had tragic consequences because it produced crippled model Hamiltonians, unfortunately considered sufficient…
Lagrangian formulation of quantum mechanical Schr\"odinger equation is developed in general and illustrated in the eigenbasis of the Hamiltonian and in the coordinate representation. The Lagrangian formulation of physically plausible…
By adding generalizations involving translations, the machinery of the quantum theory of free fields leads to the semiclassical equations of motion for a charged massive particle in electromagnetic and gravitational fields. With the…
Within the framework of the q-deformed Heisenberg algebra a dynamical equation of q-deformed quantum mechanics is discussed. The perturbative aspects of the q-deformed Schr\"odinger equation are analyzed. General representations of the…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
Free vector fields, satisfying the Lorenz condition, are investigated in details in the momentum picture of motion in Lagrangian quantum field theory. The field equations are equivalently written in terms of creation and annihilation…
The hyperplane and proper time formalisms are discussed mainly for the spin-half particles in the quantum case. A connection between these covariant Hamiltonian formalisms is established. It is showed that choosing the space-like…
We present two examples of non-Hermitian Hamiltonians which consist of an unperturbed part plus a perturbation that behaves like a vector, in the framework of PT quantum mechanics. The first example is a generalization of the recent work by…
In the limit of large quantum excitations, the classical and quantum probability distributions for a Schr\"odinger equation can be compared by using the corresponding WKBJ solutions whose rapid oscillations are averaged. This result is…
We study the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an effect of the…
Schroedinger equations with position dependent mass which are scale invariant and admit second order integrals of motion are classified.
We modify the path integral representation of exciton transport in open quantum systems such that an exact description of the quantum fluctuations around the classical evolution of the system is possible. As a consequence, the time…
The Eckart frame is used to separate out the collective rotations in the quantum three-body problem. Explicit expressions for the corresponding rotational and vibro-rotational (i.e. Coriolis) Hamiltonians are derived. Special attention is…
A modified version of relational quantum mechanics is developed based on the three following ideas. An observer can develop an internally consistent description of the universe but it will, of necessity, differ in particulars from the…
We define quantum bi-Hamiltonian systems, by analogy with the classical case, as derivations in operator algebras which are inner derivations with respect to two compatible associative structures. We find such structures by means of the…
In this second in a series of four articles we create a mathematical formalism sufficient to represent nontrivial hamiltonian quantum dynamics, including resonances. Some parts of this construction are also mathematically necessary. The…
Fradkin's representation is a general method of attacking problems in quantum field theory, having as its basis the functional approach of Schwinger. As a pedagogical illustration of that method, we explicitly formulate it for quantum…