On using the known equivalence between the presence of a position-dependent mass (PDM) in the Schr\"odinger equation and a deformation of the canonical commutation relations, a method based on...
Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry (2008)
We construct two new exactly solvable potentials giving rise to bound-state solutions to the Schr\"odinger equation, which can be written in terms of the recently introduced Laguerre- or Jacobi-type...
MODÈLE DÉGÉNÉRÉ POUR LA S. D. I. DANS LES NOYAUX IMPAIRS SPHÉRIQUES (2008)
Quesne, C., Bohigas, O., Arvieu, R.
La solution exacte pour un nombre impair de nucléons identiques, soumis à une interaction delta de surface dans des sous-couches dégénérées, est étudiée du point de vue des spectres, des...
MODÈLE DÉGÉNÉRÉ POUR LA S. D. I. DANS LES NOYAUX IMPAIRS SPHÉRIQUES (2008)
Quesne, C., Bohigas, O., Arvieu, R.
La solution exacte pour un nombre impair de nucléons identiques, soumis à une interaction delta de surface dans des sous-couches dégénérées, est étudiée du point de vue des spectres, des...
Oscillator-Morse-Coulomb mappings and algebras for constant or position-dependent mass (2007)
The bound-state solutions and the su(1,1) description of the $d$-dimensional radial harmonic oscillator, the Morse and the $D$-dimensional radial Coulomb Schr\"odinger equations are reviewed in a...
Quadratic algebras and position-dependent mass Schr\"odinger equations (2007)
During recent years, exact solutions of position-dependent mass Schr\"odinger equations have inspired intense research activities, based on the use of point canonical transformations, Lie algebraic...
A harmonic oscillator Hamiltonian augmented by a non-Hermitian \pt-symmetric part and its su(1,1) generalizations, for which a family of positive-definite metric operators was recently constructed,...
A complex periodic QES potential and exceptional points (2007)
Bagchi, B., Quesne, C., Roychoudhury, R.
We show that the complex $\cal PT$-symmetric periodic potential $V(x) = - ({\rm i} \xi \sin 2x + N)^2$, where $\xi$ is real and $N$ is a positive integer, is quasi-exactly solvable. For odd values of...
Non-Hermitian oscillator Hamiltonian and su(1,1): a way towards generalizations (2007)
The family of metric operators, constructed by Musumbu {\sl et al} (2007 {\sl J. Phys. A: Math. Theor.} {\bf 40} F75), for a harmonic oscillator Hamiltonian augmented by a non-Hermitian $\cal...
Spectrum generating algebras for position-dependent mass oscillator Schrodinger equations (2007)
The interest of quadratic algebras for position-dependent mass Schr\"odinger equations is highlighted by constructing spectrum generating algebras for a class of d-dimensional radial harmonic...
We consider a particle with a position-dependent mass, moving in a three-dimensional semi-infinite parallelepipedal or cylindrical channel under the influence of some hyperbolic potential. We show...
Lorentz-covariant deformed algebra with minimal length (2006)
The $D$-dimensional two-parameter deformed algebra with minimal length introduced by Kempf is generalized to a Lorentz-covariant algebra describing a ($D+1$)-dimensional quantized space-time. For...
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing...
Morse potential and its relationship with the Coulomb in a position-dependent mass background (2006)
Bagchi, B., Gorain, P. S., Quesne, C.
We provide some explicit examples wherein the Schr\"odinger equation for the Morse potential remains exactly solvable in a position-dependent mass background. Furthermore, we show how in such a...
Bagchi, B., Banerjee, A., Quesne, C.
To lowest order of perturbation theory we show that an equivalence can be established between a $\cal PT$-symmetric generalized quartic anharmonic oscillator model and a Hermitian position-dependent...
The $D$-dimensional $(\beta, \beta')$-two-parameter deformed algebra introduced by Kempf is generalized to a Lorentz-covariant algebra describing a ($D+1$)-dimensional quantized space-time. In the...
Hamiltonians with position-dependent mass, deformations and supersymmetry (2005)
Quesne, C., Bagchi, B., Banerjee, A., Tkachuk, V. M.
A new method for generating exactly solvable Schr\"odinger equations with a position-dependent mass is proposed. It is based on a relation with some deformed Schr\"odinger equations, which can be...
Bagchi, B., Quesne, C., Roychoudhury, R.
We formulate a systematic algorithm for constructing a whole class of Hermitian position-dependent-mass Hamiltonians which, to lowest order of perturbation theory, allow a description in terms of...
The problem of d-dimensional Schrodinger equations with a position-dependent mass is analyzed in the framework of first-order intertwining operators. With the pair (H, H_1) of intertwined...
Pseudo-Hermiticity and some consequences of a generalized quantum condition (2005)
Bagchi, B., Quesne, C., Roychoudhury, R.
We exploit the hidden symmetry structure of a recently proposed non-Hermitian Hamiltonian and of its Hermitian equivalent one. This sheds new light on the pseudo-Hermitian character of the former and...
PT-supersymmetric partner of a short-range square well (2005)
Quesne, C., Bagchi, B., Mallik, S., Bila, H., Jakubsky, V., Znojil, M.
In a box of size $L$, a spatially antisymmetric square-well potential of a purely imaginary strength ${\rm i}g$ and size $l < L$ is interpreted as an initial element of the SUSY hierarchy of solvable...
Bagchi, B., Gorain, P., Quesne, C., Roychoudhury, R.
By using the point canonical transformation approach in a manner distinct from previous ones, we generate some new exactly solvable or quasi-exactly solvable potentials for the one-dimensional...
k-Component q-deformed charge coherent states and their nonclassical properties (2005)
k-Component q-deformed charge coherent states are constructed, their (over)completeness proved and their generation explored. The q-deformed charge coherent states and the even (odd) q-deformed...
PT-symmetric supersymmetry in a solvable short-range model (2005)
Bagchi, B., Bila, H., Jakubsky, V., Mallik, S., Quesne, C., Znojil, M.
The simplest purely imaginary and piecewise constant $\cal PT$-symmetric potential located inside a larger box is studied. Unless its strength exceeds a certain critical value, all the spectrum of...
Bagchi, B., Banerjee, A., Caliceti, E., Cannata, F., Geyer, H. B., Quesne, C., ...
A brief overview is given of recent developments and fresh ideas at the intersection of PT and/or CPT-symmetric quantum mechanics with supersymmetric quantum mechanics (SUSY QM). We study the...
Dirac oscillator with nonzero minimal uncertainty in position (2004)
In the context of some deformed canonical commutation relations leading to isotropic nonzero minimal uncertainties in the position coordinates, a Dirac equation is exactly solved for the first time,...
Bagchi, B., Banerjee, A., Quesne, C., Tkachuk, V. M.
Known shape-invariant potentials for the constant-mass Schrodinger equation are taken as effective potentials in a position-dependent effective mass (PDEM) one. The corresponding shape-invariance...
Effective-mass Schroedinger equation and generation of solvable potentials (2004)
Bagchi, B., Gorain, P., Quesne, C., Roychoudhury, R.
A one-dimensional Schr\"odinger equation with position-dependent effective mass in the kinetic energy operator is studied in the framework of an $so(2,1)$ algebra. New mass-deformed versions of Scarf...
Bagchi, B., Gorain, P., Quesne, C., Roychoudhury, R.
A systematic procedure to study one-dimensional Schr\"odinger equation with a position-dependent effective mass (PDEM) in the kinetic energy operator is explored. The conventional free-particle...
We show that there exist some intimate connections between three unconventional Schr\"odinger equations based on the use of deformed canonical commutation relations, of a position-dependent effective...
Conditionally exactly solvable potential and dual transformation in quantum mechanics (2004)
We comment that the conditionally exactly solvable potential of Dutt et al. and the exactly solvable potential from which it is derived form a dual system.
We continue our previous application of supersymmetric quantum mechanical methods to eigenvalue problems in the context of some deformed canonical commutation relations leading to nonzero minimal...
Geometrical and physical properties of maths-type q-deformed coherent states for $0 (2003)
Quesne, C., Penson, K. A., Tkachuk, V. M.
We compare the geometrical and physical properties of the maths-type coherent states for $q>1$ with those of the same for $0 < q < 1$.
Disentangling q-exponentials: A general approach (2003)
We revisit the q-deformed counterpart of the Zassenhaus formula, expressing the Jackson $q$-exponential of the sum of two non-$q$-commuting operators as an (in general) infinite product of...
Even and odd q-deformed charge coherent states and their nonclassical properties (2003)
Even and odd q-deformed charge coherent states are constructed, their (over)completeness proved and their generation explored. A $D$-algebra realization of the SU$_q$(1,1) generators is given in...
In the context of a two-parameter $(\alpha, \beta)$ deformation of the canonical commutation relation leading to nonzero minimal uncertainties in both position and momentum, the harmonic oscillator...
Jackson's q-exponential as the exponential of a series (2003)
Jackson's q-exponential is expressed as the exponential of a series whose coefficients are obtained in closed form. Such a relation is used to derive some properties of the q-exponential.
Maths-type q-deformed coherent states for q > 1 (2003)
Quesne, C., Penson, K. A., Tkachuk, V. M.
Maths-type q-deformed coherent states with $q > 1$ allow a resolution of unity in the form of an ordinary integral. They are sub-Poissonian and squeezed. They may be associated with a harmonic...
Fractional supersymmetric quantum mechanics of order $\lambda$ is realized in terms of the generators of a generalized deformed oscillator algebra and a Z$_{\lambda}$-grading structure is imposed on...
Non-Hermitian Hamiltonians with real and complex eigenvalues: An sl(2,C) approach (2002)
Potential algebras are extended from Hermitian to non-Hermitian Hamiltonians and shown to provide an elegant method for studying the transition from real to complex eigenvalues for a class of...
Infinite square well and periodic trajectories in classical mechanics (2002)
Bagchi, B., Mallik, S., Quesne, C.
We examine the classical problem of an infinite square well by considering Hamilton's equations in one dimension and Hamilton-Jacobi equation for motion in two dimensions. We illustrate, by means of...
New q-deformed coherent states with an explicitly known resolution of unity (2002)
We construct a new family of q-deformed coherent states $|z>_q$, where $0 < q < 1$. These states are normalizable on the whole complex plane and continuous in their label $z$. They allow the...
Pseudo-Hermiticity, weak pseudo-Hermiticity and eta-orthogonality condition (2002)
We discuss certain features of pseudo-Hermiticity and weak pseudo-Hermiticity conditions and point out that, contrary to a recent claim, there is no inconsistency if the correct orthogonality...
Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework (2002)
We show that complex Lie algebras (in particular sl(2,C)) provide us with an elegant method for studying the transition from real to complex eigenvalues of a class of non-Hermitian Hamiltonians:...
PT-symmetric square well and the associated SUSY hierarchies (2002)
Bagchi, B., Mallik, S., Quesne, C.
The PT-symmetric square well problem is considered in a SUSY framework. When the coupling strength $Z$ lies below the critical value $Z_0^{\rm (crit)}$ where PT symmetry becomes spontaneously broken,...
Pseudosupersymmetric quantum mechanics (PsSSQM), based upon the use of pseudofermions, was introduced in the context of a new Kemmer equation describing charged vector mesons interacting with an...
Reducibility and bosonization of parasupersymmetric and orthosupersymmetric quantum mechanics (2002)
Order-$p$ parasupersymmetric and orthosupersymmetric quantum mechanics are shown to be fully reducible when they are realized in terms of the generators of a generalized deformed oscillator algebra...
Extending the supersymmetric method proposed by Tkachuk to the complex domain, we obtain general expressions for superpotentials allowing generation of quasi-exactly solvable PT-symmetric potentials...
Connection between type B (or C) and F factorizations and construction of algebras (2001)
In a recent paper (Del Sol Mesa A and Quesne C 2000 J. Phys. A: Math. Gen. 33 4059), we started a systematic study of the connections among different factorization types, suggested by Infeld and...
Creation and annihilation operators and coherent states for the PT-symmetric oscillator (2001)
We construct two commuting sets of creation and annihilation operators for the PT-symmetric oscillator. We then build coherent states of the latter as eigenstates of such annihilation operators by...
Generalized Coherent States Associated with the $C_{\lambda}$-Extended Oscillator (2001)
Two new types of coherent states associated with the $C_{\lambda}$-extended oscillator, where $C_{\lambda}$ is the cyclic group of order $\lambda$, are introduced. They satisfy a unity resolution...
A discrete completeness relation and a continuous one with a positive measure are found for the photon-added squeezed vacuum states. Extension to the photon-added squeezed one-photon states is...
Generalized coherent states associated with the C_{\lambda}-extended oscillator (2001)
Two new types of coherent states associated with the C_{\lambda}-extended oscillator, where C_{\lambda} is the cyclic group of order \lambda, are introduced. The first ones include as special cases...
Generalized Continuity Equation and Modified Normalization in PT-Symmetric Quantum Mechanics (2001)
Bagchi, B., Quesne, C., Znojil, M.
The continuity equation relating the change in time of the position probability density to the gradient of the probability current density is generalized to PT-symmetric quantum mechanics. The...
A PT Symmetric QES Partner to the Khare Mandal Potential With Real Eigen Values (2001)
Bagchi, B., Mullik, S., Quesne, C., Roychoudhury, R.
We consider a PT Symmetric Partner to Khare Mandal's recently proposed non-Hermitian potential with complex eigen values. Our potential is Quasi-Exactly solvable and is shown to possess only real...
Bagchi, B., Mallik, S., Quesne, C.
We analyze a set of three PT-symmetric complex potentials, namely harmonic oscillator, generalized Poschl-Teller and Scarf II, all of which reveal a double series of energy levels along with the...
Generating Complex Potentials with Real Eigenvalues in Supersymmetric Quantum Mechanics (2001)
Bagchi, B., Mallik, S., Quesne, C.
In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians, we analyze three sets of complex potentials with real spectra, recently derived by a potential algebraic approach based...
Para, pseudo, and orthosupersymmetric quantum mechanics and their bosonization (2000)
We consider the problem of bosonizing supersymmetric quantum mechanics (SSQM) and some of its variants, i.e., of realizing them in terms of only boson-like operators without fermion-like ones. In the...
Spectrum generating algebra and coherent states of the $C_{\lambda}$-extended oscillator (2000)
$C_{\lambda}$-extended oscillator algebras, generalizing the Calogero-Vasiliev algebra, where $C_{\lambda}$ is the cyclic group of order $\lambda$, have recently proved very useful in the context of...
The powerful group theoretical formalism of potential algebras is extended to non-Hermitian Hamiltonians with real eigenvalues by complexifying so(2,1), thereby getting the complex algebra sl(2,\C)...
The $C_{\lambda}$-extended oscillator spectrum generating algebra is shown to be a $C_{\lambda}$-extended $(\lambda-1)$th-degree polynomial deformation of su(1,1). Its coherent states are...
Connection Between Type A and E Factorizations and Construction of Satellite Algebras (2000)
Recently, we introduced a new class of symmetry algebras, called satellite algebras, which connect with one another wavefunctions belonging to different potentials of a given family, and...
$C_{\lambda}$-extended oscillator algebras generalizing the Calogero-Vasiliev algebra, where $C_{\lambda}$ is the cyclic group of order $\lambda$, are studied both from mathematical and applied...
PT-symmetric sextic potentials (2000)
Bagchi, B., Cannata, F., Quesne, C.
The family of complex PT-symmetric sextic potentials is studied to show that for various cases the system is essentially quasi-solvable and possesses real, discrete energy eigenvalues. For a...
We comment on a recent paper by Chen, Liu, and Ge (J. Phys. A: Math. Gen. 31 (1998) 6473), wherein a nonlinear deformation of su(1,1) involving two deforming functions is realized in the exactly...
C$_{\lambda}$-extended oscillator algebras, where C$_{\lambda}$ is the cyclic group of order $\lambda$, are introduced and realized as generalized deformed oscillator algebras. For $\lambda=2$, they...
Interpretation and Extension of the Green's Ansatz for Paraparticles (1999)
The anomalous bilinear commutation relations satisfied by the components of the Green's ansatz for paraparticles are shown to derive from the comultiplication of the paraboson or parafermion algebra....
suq(2)-Invariant Harmonic Oscillator (1999)
We propose a q-deformation of the su(2)-invariant Schrodinger equation of a spinless particle in a central potential, which allows us not only to determine a deformed spectrum and the corresponding...
suq(2)-Invariant Schrodinger Equation of the Three-Dimensional Harmonic Oscillator (1999)
We propose a q-deformation of the su(2)-invariant Schrodinger equation of a spinless particle in a central potential, which allows us not only to determine a deformed spectrum and the corresponding...
$GL_h(n) \times GL_{h'}(m)$-covariant (hh')-bosonic (or (hh')-fermionic) algebras ${\cal A}_{hh'\pm}(n,m)$ are built in terms of the corresponding R_h and $R_{h'}$-matrices by contracting the...
We study in detail the spectrum of the bosonic oscillator Hamiltonian associated with the $C_3$-extended oscillator algebra \algthree, where $C_3$ denotes a cyclic group of order three, and classify...
On Jordanian U_{h,\alpha}(gl(2)) Algebra and Its T Matrices Via a Contraction Method (1998)
The $R_h^{j_1;j_2}$ matrices of the Jordanian U$_h$(sl(2)) algebra at arbitrary dimensions may be obtained from the corresponding $R_q^{j_1;j_2}$ matrices of the standard $q$-deformed U$_q$(sl(2))...
Nonstandard GL_h(n) quantum groups and contraction of covariant q-bosonic algebras (1998)
$GL_h(n) \times GL_h(m)$-covariant $h$-bosonic algebras are built by contracting the $GL_q(n) \times GL_q(m)$-covariant $q$-bosonic algebras considered by the present author some years ago. Their...
Contribution to the Analysis of the Alpha/Beta Interface in Some Titanium Alloys. (1998)
Servant, C., Quesne, C., Baudin, T., Penelle, R.
In (alpha + beta) titanium alloys, the interface between the alpha and beta phases has been widely studied, and many conflicting results have been published concerning the formation of an interface...
We apply the exchange operator formalism in polar coordinates to a one-parameter family of three-body problems in one dimension and prove the integrability of the model both with and without the...
Some time ago, Rideau and Winternitz introduced a realization of the quantum algebra su_q(2) on a real two-dimensional sphere, or a real plane, and constructed a basis for its representations in...
C_{\lambda}-extended oscillator algebra and parasupersymmetric quantum mechanics (1998)
The C_{\lambda}-extended oscillator algebra is generated by {1,a,a^{\dagger},N,T}, where T is the generator of the cyclic group C_{\lambda} of order \lambda. It can be realized as a generalized...
Unitary Representations of Su_q(2) on the Plane for q in R+ or Generic q in S1 (1998)
Some time ago, Rideau and Winternitz introduced a realization of the quantum algebra su_q(2) on a real two-dimensional sphere, or a real plane, and constructed a basis for its representations in...
The exchange operator formalism previously introduced for the Calogero problem is extended to the three-body Calogero-Marchioro-Wolfes one. In the absence of oscillator potential, the Hamiltonian of...
$C_{\lambda}$-extended harmonic oscillator and (para)supersymmetric quantum mechanics (1998)
$C_{\lambda}$-extended oscillator algebras are realized as generalized deformed oscillator algebras. For $\lambda = 3$, the spectrum of the corresponding bosonic oscillator Hamiltonian is shown to...
Coloured Hopf algebras and their duals (1997)
Coloured Hopf algebras, related to the coloured Yang-Baxter equation, are reviewed, as well as their duals. The special case of coloured quantum universal enveloping algebras provides a coloured...
We extend the notion of dually conjugate Hopf (super)algebras to the coloured Hopf (super)algebras ${\cal H}^c$ that we recently introduced. We show that if the standard Hopf (super)algebras ${\cal...
Generalized Morse Potential: Symmetry and Satellite Potentials (1997)
Mesa, A. Del Sol, Quesne, C., Smirnov, Yu. F.
We study in detail the bound state spectrum of the generalized Morse potential~(GMP), which was proposed by Deng and Fan as a potential function for diatomic molecules. By connecting the...
Three-body generalization of the Sutherland model with internal degrees of freedom (1997)
A generalized spin Sutherland model including a three-body potential is proposed. The problem is analyzed in terms of three first-order differential-difference operators, obtained by combining SUSYQM...
Three-body Generalizations of the Sutherland Problem (1997)
The three-particle Hamiltonian obtained by replacing the two-body trigonometric potential of the Sutherland problem by a three-body one of a similar form is shown to be exactly solvable. When written...
Coloured quantum universal enveloping algebras (1997)
We define some new algebraic structures, termed coloured Hopf algebras, by combining the coalgebra structures and antipodes of a standard Hopf algebra set $\cal H$, corresponding to some parameter...
Quite recently, a ``coloured'' extension of the Yang-Baxter equation has appeared in the literature and various solutions of it have been proposed. In the present contribution, we introduce a...
Some new algebraic structures related to the coloured Yang-Baxter equation, and termed coloured Hopf algebras, are reviewed. Coloured quantum universal enveloping algebras of Lie algebras are defined...
Zero-energy states for a class of quasi-exactly solvable rational potentials (1997)
Quasi-exactly solvable rational potentials with known zero-energy solutions of the Schro\" odinger equation are constructed by starting from exactly solvable potentials for which the Schr\" odinger...