Supersymmetric and Shape-Invariant Generalization for Nonresonant and Intensity-Dependent Jaynes-Cummings Systems

A class of shape-invariant bound-state problems which represent transition in a two-level system introduced earlier are generalized to include arbitrary energy splittings between the two levels as well as intensity-dependent interactions. We show that the couple-channel Hamiltonians obtained correspond to the generalizations of the nonresonant and intensity-dependent nonresonant Jaynes-Cummings Hamiltonians, widely used in quantized theories of laser. In this general context, we determine the eigenstates, eigenvalues, the time evolution matrix and the population inversion matrix factor.Comment: A combined version of quant-ph/0005045 and quant-ph/0005046. 24 pages, LATE

Generalized Ladder Operators for Shape-invariant Potentials

A general form for ladder operators is used to construct a method to solve bound-state Schr\"odinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the elegance and the utility of the method we use it to obtain energy spectra and eigenfunctions for the one-dimensional harmonic oscillator and Morse potentials and for the radial harmonic oscillator and Coulomb potentials.Comment: in Revte

A Generalized Jaynes-Cummings Hamiltonian and Supersymmetric Shape-Invariance

A class of shape-invariant bound-state problems which represent two-level systems are introduced. It is shown that the coupled-channel Hamiltonians obtained correspond to the generalization of the Jaynes-Cummings Hamiltonian

Hypoglycemia in Pregnancy

Hypoglycemia is considered when glycemia values fall below 60 mg/dl and is associated with increased maternal-fetal morbidity and mortality. In a diabetic pregnancy this complication can result from a decrease in caloric ingestion relative to administered insulin. Hypoglycemia can present as a simple adrenergic response or as a neuroglicopenic response that can lead to maternal death and stillbirth. This is the reason why it can rapidly evolve into an obstetric emergency. It is important to possess a pre-defined protocol to guide healthcare professionals regarding the rapid management of this situation. The authors review the scientific literature on the subject of hypoglycemia in pregnancy and propose a protocol to be applied in this situation

An Algebraic q-Deformed Form for Shape-Invariant Systems

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 construct an alternative q-deformed model that preserve the shape-invariance property presented by primary system. q-deformed generalizations of Morse, Scarf, and Coulomb potentials are given as examples

Algebraic Nature of Shape-Invariant and Self-Similar Potentials

Self-similar potentials generalize the concept of shape-invariance which was originally introduced to explore exactly-solvable potentials in quantum mechanics. In this article it is shown that previously introduced algebraic approach to the latter can be generalized to the former. The infinite Lie algebras introduced in this context are shown to be closely related to the q-algebras. The associated coherent states are investigated.Comment: 8 page

Supersymmetric Jaynes-Cummings model and its exact solutions

The super-algebraic structure of a generalized version of the Jaynes-Cummings model is investigated. We find that a Z2 graded extension of the so(2,1) Lie algebra is the underlying symmetry of this model. It is isomorphic to the four-dimensional super-algebra u(1/1) with two odd and two even elements. Differential matrix operators are taken as realization of the elements of the superalgebra to which the model Hamiltonian belongs. Several examples with various choices of superpotentials are presented. The energy spectrum and corresponding wavefunctions are obtained analytically.Comment: 12 pages, no figure