Related papers: Generalized ladder operators for the perturbed har…
We construct a generalised expression for the normal ordering of (a+a^{\dagger})^{m} for integral values of m and use the result to study the quantum anharmonic oscillator problem in the Heisenberg approach. In particular, we derive…
We prove a reducibility result for a quantum harmonic oscillator in arbitrary dimensions with arbitrary frequencies perturbed by a linear operator which is a polynomial of degree two in $x_j$, $-i \partial_j$ with coefficients which depend…
The type III Hermite $X_m$ exceptional orthogonal polynomial family is generalized to a double-indexed one $X_{m_1,m_2}$ (with $m_1$ even and $m_2$ odd such that $m_2 > m_1$) and the corresponding rational extensions of the harmonic…
In this paper we introduce a new method for constructing coherent states for 2D harmonic oscillators. In particular, we focus on both the isotropic and commensurate anisotropic instances of the 2D harmonic oscillator. We define a new set of…
Supersymmetric quantum mechanics has many applications, and typically uses a raising and lowering operator formalism. For one dimensional problems, we show how such raising and lowering operators may be generalized to include an arbitrary…
We consider a general discrete Sobolev inner product involving the Hahn difference operator, so this includes the well--known difference operators $\mathscr{D}_{q}$ and $\Delta$ and, as a limit case, the derivative operator. The objective…
Harmonic oscillator coherent states are well known to be the analogue of classical states. On the other hand, nonlinear and generalised coherent states may possess nonclassical properties. In this article, we study the nonclassical…
In this paper, we construct nonlinear coherent states for the generalized isotonic oscillator and study their non-classical properties in-detail. By transforming the deformed ladder operators suitably, which generate the quadratic algebra,…
We complete the construction of raising and lowering operators, given in a previous work, for the orthogonal polynomials of hypergeometric type on non-homogeneous lattice, and extend these operators to the generalized orthogonal…
Conventional weak-coupling perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multiple-scale perturbation theory avoids such problems by implicitly performing an…
The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator is developed. Based upon the $\hbar$-expansions and suitable quantization conditions a new…
This note presents the classification of ladder operators corresponding to the class of rational extensions of the harmonic oscillator. We show that it is natural to endow the class of rational extensions and the corresponding intertwining…
A new totally algebraic formalism based on general, abstract ladder operators has been proposed. This approach heavily grounds in the superoperator formalism of Primas. However it is necessary to introduce many improvements in his…
Morse oscillator is one of the known solvable potentials which attracts many applications in quantum mechanics especially in quantum chemistry. One of the interesting results of this study is the generation of ladder operators for Morse…
We show that various kinds of one-photon quantum states studied in the field of quantum optics admit ladder operator formalisms and have the generally deformed oscillator algebraic structure. The two-photon case is also considered. We…
The problem of construction of ladder operators for rationally extended quantum harmonic oscillator (REQHO) systems of a general form is investigated in the light of existence of different schemes of the Darboux-Crum-Krein-Adler…
Ladder operators are useful, if not essential, in the analysis of some given physical system since they can be used to find easily eigenvalues and eigenvectors of its Hamiltonian. In this paper we extend our previous results on abstract…
Using the {\it nonlinear coherent states method}, a formalism for the construction of the coherent states associated to {\it "inverse bosonic operators"} and their dual family has been proposed. Generalizing the approach, the "inverse of…
In this paper we generalize the spin-raising and lowering operators of spin-weighted spherical harmonics to linear-in-$\gamma$ spin-weighted spheroidal harmonics where $\gamma$ is an additional parameter present in the second order ordinary…
We investigate a class of Lagrangians that admit a type of perturbed harmonic oscillator which occupies a special place in the literature surrounding perturbation theory. We establish explicit and generalized geometric conditions for the…