相关论文: Deformed Heisenberg algebra with upper bound of mo…
A deformation of Heisenberg algebra induces among other consequences a loss of Hermiticity of some operators that generate this algebra. Therefore, these operators are not Hermitian, nor is the Hamiltonian operator built from them. In the…
The relation between nonlinear algebras and linear ones is established. For one-dimensional nonlinear deformed Heisenberg algebra with two operators we find the function of deformation for which this nonlinear algebra can be transformed to…
In this paper we will demonstrate that like the existence of a minimum measurable length, the existence of a maximum measurable momentum, also influence all quantum mechanical systems. Beyond the simple one dimensional case, the existence…
Starting from generalized position operators, we derive complex and quaternionic angular momentum operators along with their commutation algebra as well. These algebras differ from the standard Hermitian ones, especially in terms of…
Perivolaropoulos has recently proposed a position-deformed Heisenberg algebra which includes a maximal length [Phys.Rev.95, 103523 (2017)]. He has shown that this length scale naturally emerges in the context of cosmological particle's…
A one-dimensional deformed Heisenberg algebra $[X,P]=if(P)$ is studied. We answer the question: For what function of deformation $f(P)$ there exists a nonzero minimal uncertainty in position (minimal length). We also find an explicit…
A new approach in solution of simple quantum mechanical problems in deformed space with minimal length is presented. We propose the generalization of Schro\"edinger equation in momentum representation on the case of deformed Heisenberg…
With the help of the deformed Heisenberg algebra involving Klein operator, we construct the minimal set of linear differential equations for the (2+1)-dimensional relativistic field with arbitrary fractional spin, whose value is defined by…
We present a definition of the two-sided inverse of position operator in general case of deformed Heisenberg algebra leading to minimal length. Energy spectrum and eigenfunctions in momentum space for 1D Coulomb-like potential in deformed…
A universality of deformed Heisenberg algebra involving the reflection operator is revealed. It is shown that in addition to the well-known infinite-dimensional representations related to parabosons, the algebra has also finite-dimensional…
We show how one can construct a differential calculus over an algebra where position variables x and momentum variables p have be defined. As the simplest example we consider the one-dimensional q-deformed Heisenberg algebra. This algebra…
For composite systems made of $N$ different particles living in a space characterized by the same deformed Heisenberg algebra, but with different deformation parameters, we define the total momentum and the center-of-mass position to first…
We solve the problem of Fourier transformation for the one-dimensional $q$-deformed Heisenberg algebra. Starting from a matrix representation of this algebra we observe that momentum and position are unbounded operators in the Hilbert…
The dynamical algebra of the q-deformed harmonic oscillator is constructed. As a result, we find the free deformed Hamiltonian as well as the Hamiltonian of the deformed oscillator as a complicated, momentum dependent interaction…
This lecture consists of two sections. In section 1 we consider the simplest version of a q-deformed Heisenberg algebra as an example of a noncommutative structure. We first derive a calculus entirely based on the algebra and then formulate…
We describe generally deformed Heisenberg algebras in one dimension. The condition for a generalized Leibniz rule is obtained and solved. We analyze conditions under which deformed quantum-mechanical problems have a Fock-space…
A general deformation of the Heisenberg algebra is introduced with two deformed operators instead of just one. This is generalised to many variables, and permits the simultaneous existence of coherent states, and the transposition of…
Quantum gravity theories predict a minimal length at the order of magnitude of the Planck length, under which the concepts of space and time lose every physical meaning. In quantum mechanics, the insurgence of such minimal length can be…
Non-commutative Quantum Mechanics in 3D is investigated in the framework of the abelian Drinfeld twist which deforms a given Hopf algebra while preserving its Hopf algebra structure. Composite operators (of coordinates and momenta) entering…
We consider a real scalar field and a Majorana fermion field to construct a supersymmetric quantum theory of free fermion fields based on the deformed Heisenberg algebra $[x,p]=i\hbar\big(1-\beta p+2\beta^{2}p^{2}\big)$, where $\beta $ is a…