Related papers: The photon position operator (non-commuting) and i…
In this paper we suggest a configuration of photons consistent with a spin $\hbar$, and a configuration of the fermions coherent with a spin $\hbar/2$. These suggested configurations open the way to further analyses which lead to the…
Hamiltonians describing the relativistic quantum dynamics of a particle with an arbitrary spin are shown to exhibit a supersymmetric structure when the even and odd elements of the Hamiltonian commute. For such supersymmetric Hamiltonians…
We obtain and investigate the regular eigenfunctions of simple differential operators x^r d^{r+1}/dx^{r+1}, r=1, 2, ... with the eigenvalues equal to one. With the help of these eigenfunctions we construct a non-unitary analogue of boson…
We calculate the uncertainties in the position and momentum of a particle in the 1D potential V(x)=F|x|, F>0, when the position and momentum operators obey the deformed commutation relation [x,p]=i\hbar(1+\beta p^2), \beta>0. As in the…
An operator formalism is developed for a description of charged electron-hole complexes in magnetic fields. A novel unitary transformation of the Hamiltonian that allows one to partially separate the center-of-mass and internal motions is…
Abbreviated Abstract: We study correlated states in a circular and linear-chain configuration of identical two-level atoms containing the energy of a single quasi-resonant photon in the form of a collective excitation, where the collective…
We analyze some features of alternative Hermitian and quasi-Hermitian quantum descriptions of simple and bipartite compound systems. We show that alternative descriptions of two interacting subsystems are possible if and only if the metric…
On the basis of the f-deformed oscillator formalism, we propose to construct nonlinear coherent states for Hamiltonian systems having linear and quadratic terms in the the number operator by means of the two following definitions: i) as…
The physical meaning of the operators is not reducible to the intrinsic relations of the quantum system, since unitary transformations can find other operators satisfying the exact same relations. The physical meaning is determined…
We study the $N=2$ string with a real structure on the $(2,2)$ spacetime, using BRST methods. Several new features emerge. In the diagonal basis, the operator $\exp(\lambda \int^z J^{\rm tot})$, which is associated with the moduli for the…
Although non-commutativity of a certain set of quantum operators (e.g., creation/annihilation operators and Pauli spin operators) has been shown experimentally in recent years, the commu- tation relation for the position and the momentum…
We consider the Hamiltonian $H$ of a particle in one dimension with a position dependent mass for which we apply the recent strategy of the so-called {\em abstract ladder operators}, in the attempt to find its eigenvalues and eigenvectors.…
The minimal-length paradigm is a cornerstone of quantum gravity phenomenology. Recently, it has been demonstrated that minimal-length quantum mechanics can alternatively be described as an undeformed theory set on a nontrivial momentum…
In this paper we study in details a system of two weakly coupled harmonic oscillators. This system may be viewed as a simple model for the interaction between a photon and a photodetector. We obtain exact solutions for the general case. We…
We study the theory of the (1/2,0)+(0,1/2) representation in helicity basis. Helicity eigenstates are not the parity eigenstates. This is in accordance with the consideration of Berestetskii, Lifshitz and Pitaevskii. Relations to the…
Non-hermiticity presents a vast newly opened territory that harbors new physics and applications such as lasing and sensing. However, only non-Hermitian systems with real eigenenergies are stable, and great efforts have been devoted in…
This paper revisits the quantum mechanics for one photon from the modern viewpoint and by the geometrical method. Especially, besides the ordinary (rectangular) momentum representation, we provide an explicit derivation for the other two…
In this investigation, the displacement operator is revisited. We established a connection between the Hermitian version of this operator with the well-known Weyl ordering. Besides, we characterized the quantum properties of a simple…
Relativistic electronic properties of a nanospring under a static magnetic field are theoretically investigated in the present study. The wave equation accounting for the spin-orbit interaction is derived for the nanospring as a special…
A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review…