Related papers: Self-Similar Potentials and q-Coherent States
A general procedure for constructing coherent states, which are eigenstates of annihilation operators, related to quantum mechanical potential problems, is presented. These coherent states, by construction are not potential specific and…
Using a recently proposed classification for the primary translationally shape invariant potentials, we show that the exact quantization rule formulated by Ma and Xu is equivalent to the supersymmetric JWKB quantization condition. The…
Although eigenspectra of one dimensional shape invariant potentials with unbroken supersymmetry are easily obtained, this procedure is not applicable when the parameters in these potentials correspond to broken supersymmetry, since there is…
A square potential well with position-dependent mass is studied for bound states. Applying appropriate matching conditions, a transcendental equation is derived for the energy eigenvalues. Numerical results are presented graphically and the…
The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as…
We give two conditionally exactly solvable inverse power law potentials whose linearly independent solutions include a sum of two confluent hypergeometric functions. We notice that they are partner potentials and multiplicative shape…
The Poincar\'e-covariant quantum-field-theoretic description of bound states by the homogeneous Bethe-Salpeter equation usually exhibits an intrinsic complexity that can be attenuated by allowing this formalism to undergo various…
A new kind of q-deformed charged coherent states is constructed in Fock space of two-mode q-boson system with su_{q}(2) covariance and a resolution of unity for these states is derived. We also present a simple way to obtain these coherent…
We show that the method developed by Gangopadhyaya, Mallow, and their coworkers to deal with (translationally) shape invariant potentials in supersymmetric quantum mechanics and consisting in replacing the shape invariance condition, which…
Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…
A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q-deformed ladder operators. We show these new ladder operators satisfy new q-deformed commutation relations. In this context we…
Let E = F(v) be the ground-state eigenvalue of the Schroedinger Hamiltonian H = -Delta + vf(x), where the potential shape f(x) is symmetric and monotone increasing for x > 0, and the coupling parameter v is positive. If the 'kinetic…
We consider two families of extensions of the oscillator in a $d$-dimensional constant-curvature space and analyze them in a deformed supersymmetric framework, wherein the starting oscillator is known to exhibit a deformed shape invariance…
The von Neumann type subsystems of $q$-deformed coherent states are considered. The completeness of such subsystems is proved.
A general approach for constructing multidimensional quasi-exactly solvable (QES) potentials with explicitly known eigenfunctions for two energy levels is proposed. Examples of new QES potentials are presented.
Besides the standard quantum version of the Coulomb/Kepler problem, an alternative quantum model with not too dissimilar phenomenological (i.e., spectral and scattering) as well as mathematical (i.e., exact-solvability) properties may be…
We explore geometric phases of coherent states and some of their properties. A better and elegant expression of geometric phase for coherent state is derived. It is used to obtain the explicit form of the geometric phase for entangled…
Starting from deformed quantum Heisenberg Lie algebras some realizations are given in terms of the usual creation and annihilation operators of the standard harmonic oscillator. Then the associated algebra eigenstates are computed and give…
We suppose: (1) that the ground-state eigenvalue E = F(v) of the Schroedinger Hamiltonian H = -Delta + vf(x) in one dimension is known for all values of the coupling v > 0; and (2) that the potential shape can be expressed in the form f(x)…
Complex potentials are constructed as Darboux-deformations of short range, radial nonsingular potentials. They behave as optical devices which both refracts and absorbs light waves. The deformation preserves the initial spectrum of energies…