Nonperturbative approach to potentials in impenetrable boxes based on quasi-exact solvability

In this work we develop an approach to obtain analytical expressions for potentials in an impenetrable box. In this kind of system the expression has the advantage of being valid for arbitrary values of the box length, and respect the correct quantum limits. The similarity of this kind of problem with the quasi exactly solvable potentials is explored in order to accomplish our goals. Problems related to the break of symmetries and simultaneous eigenfunctions of commuting operators are discussed.

Exact solvability of potentials with spatially dependent effective masses

We discuss the relationship between exact solvability of the Schroedinger equation, due to a spatially dependent mass, and the ordering ambiguity. Some examples show that, even in this case, one can find exact solutions. Furthermore, it is demonstrated that operators with linear dependence on the momentum are nonambiguous. (C) 2000 Elsevier Science B.V.

On the solvability of implicit differential inclusions

In the paper, the set-valued covering mappings are studied. The statements on solvability, solution estimates, and well-posedness of inclusions with conditionally covering mappings are proved. The results obtained are applied to the investigation of differential inclusions unsolved for the unknown function. The statements on solvability, solution estimates, and well-posedness of these inclusions are derived.

General structures of Hamiltonian hierarchies

Three dimensional exactly solvable quantum potentials for which an extra term of form 1/r(2) has been added are shown to maintain their functional form which allows the construction of the Hamiltonian hierarchy and the determination of the spectra of eigenvalues and eigenfunctions within the Supersymmetric Quantum Mechanics formalism. For the specific cases of the harmonic oscillator and the Coulomb potentials, known as pseudo-harmonic oscillator and pseudo-Coulomb potentials, it is shown here that the inclusion of the new term corresponds to rescaling the angular momentum and it is responsible for maintaining their exact solvability.

Multistable behavior above synchronization in a locally coupled Kuramoto model

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Approximate expression for the energy of a D-dimensional anharmonic oscillator

An approximate expression is constructed for the energy of an anharmonic potential with centrifugal barrier. In order to obtain such an analytical expression, the quasi-exact solvability is used and then a fitting of these exact solutions is done.

Hamiltonian hierarchy of pseudo-potentials

The general structure of the Hamiltonian hierarchy of the pseudo-Coulomb and pseudo-Harmonic potentials is constructed by the factorization method within the supersymmetric quantum mechanics (SQMS) formalism. The excited states and spectra of eigenfunctions of the potentials are obtained through the generation of the members of the hierarchy. It is shown that the extra centrifugal term added to the Coulomb and Harmonic potentials maintain their exact solvability.

So(2,1) Lie algebra and the Green's functions for the conditionally exactly solvable potentials

The Green's functions of the recently discovered conditionally exactly solvable potentials are computed. This is done through the use of a second-order differential realization of the so(2,1) Lie algebra. So we present the dynamical symmetry underlying the solvability of such potentials and show that they belong to a general class of solvable and partially solvable potentials. © 1994 The American Physical Society.

Problemas de valor de contorno não clássicos: uma abordagem usando funções de Green

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Measure Functional Differential Equations in the Space of Functions of Bounded Variation

We establish general conditions for the unique solvability of nonlinear measure functional differential equations in terms of properties of suitable linear majorants.

Dynamical algebra of quasi-exactly-solvable potentials

We show that by using second-order differential operators as a realization of the so(2,1) Lie algebra, we can extend the class of quasi-exactly-solvable potentials with dynamical symmetries. As an example, we dynamically generate a potential of tenth power, which has been treated in the literature using other approaches, and discuss its relation with other potentials of lowest orders. The question of solvability is also studied. © 1991 The American Physical Society.

Organização da demanda de um Centro de Especialidades Odontológicas

Introduction: Secondary care in oral health in Brazil is still a little researched topic. Objective: The aim of this study was to analyze the resolution of dental services in SUS based on the referral to secondary attention and backreferral to primary attention. Methodology: It’s a descriptive, quantitative study that used secondary data collected from dental records of patients seen at Centre of Dental Specialties (Ceo) in a city of São Paulo State. Result: It was analyzed 1030 dental records. Just 1236 proceedings received referral to Ceo and among then, 86.4% showed the first attendance on Basic Health Unity (UBS) through spontaneous demand and 50.4% (n=623) received referral to endodontic treatment. There was evasion of 2.27% of studied population (n=28) on the first specialized consultation. Among 1208 proceedings that started the treatment in Ceo, 62.6% (n=757) were finalized and received back-referral to primary attention, that finalized 61.1% (n=463) of proceedings. To conclude the treatment, considering the time spent in Ceo and primary attention, there was variation according to specialty: periodontics – 62 days (sd ±68) and endodontics – 71 days (sd ±51.8), requiring 3 consultations in average, regardless specialty. Conclusion: The Centre of Dental Specialties gave referral and attention to the majority of demand, regardless specialty. However, there are many cases of evasion during dental treatment, alerting managers to develop methods to entice these patients, reducing service expenses and raising solvability of dental procedures previously initiated.