Using an iterative construction of the first-order intertwining technique, we find k- parametric families of exactly solvable anharmonic oscillators whose spectra consist of a part isospectral to the oscillator plus k additional levels at arbitrary positions below E0D 1 . It is seen that the 'natural' ladder operators for these systems give place to polynomial nonlinear algebras, and it is shown that these algebras can be linearized. The coherent states construction is performed in the nonlinear and linearized cases.

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Higher-order SUSY, linearized nonlinear Heisenberg algebras and coherent states

An approximate solution of the Schrodinger equation for the generalized Hulthen potential with non-zero angular quantum number is solved. The bound state energy eigenvalues and eigenfunctions are obtained in terms of Jacobi polynomials. The Nikiforov–Uvarov method is used in the computations. We have considered the time-independent Schrodinger equation with the associated form of Hulthen potential which simulate the effect of the centrifugal barrier for any l-state. The energy levels of the used Hulthen potential gives satisfactory values for the non-zero angular momentum as the generalized Hulthen effective potential.

Approximate Eigenvalue and Eigenfunction Solutions for the Generalized Hulthén Potential with any Angular Momentum

Hamiltonian hierarchy and the Hulthén potential

Morse potential energy spectra through the variational method and supersymmetry

We present a new approximation scheme for the centrifugal term to solve the Schrodinger equation with the Hulthen potential for any arbitrary l -state by means of a mathematical Nikiforov-Uvarov (NU) method. We obtain the bound-state energy eigenvalues and the normalized corresponding eigenfunctions expressed in terms of the Jacobi polynomials or hypergeometric functions for a particle exposed to this potential field. Our numerical results of the energy eigenvalues are found to be in high agreement with those results obtained by using the program based on a numerical integration procedure. The s -wave (l = 0analytic solution for the binding energies and eigenfunctions of a particle are also calculated. The physical meaning of the approximate analytical solution is discussed. The present approximation scheme is systematic and accurate.

An improved approximation scheme for the centrifugal term and the Hulthén potential

The formalism of supersymmetric quantum mechanics provides us with the eigenfunctions to be used in the variational method to obtain the eigenvalues for the Hulthen potential.

Supersymmetry, variational method and hulthen potential

Supersymmetric variational energies of 3d confined potentials

In this work we introduce a method to determine the time dependent probability density for the one-dimensional Fokker–Planck equation. The treatment is based in an analysis of the Schrodinger equation through the variational method associated to the formalism of supersymmetric quantum mechanics (SQM). The approach uses an ansatz for the superpotential which allows us to obtain the trial functions of the variational method. The hierarchy of effective Hamiltonians permits us to determine the variational eigenfunctions and energies of the excited states to the evaluation of the probability. The symmetric bistable potential is used to illustrate the approach whose results are compared with results obtained by the state-dependent diagonalization method and by direct numerical calculation.

Variational supersymmetric approach to evaluate Fokker–Planck probability

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.

Hamiltonian hierarchy of pseudo-potentials

Pocos de potenciais quadrados tem sido bastante explorados, tanto do ponto de vista de aplicacao como introducao didatica a mecânica quântica. Existem bem poucos potenciais desse tipo que sao tratados analiticamente na literatura, embora varias geometrias envolvendo esses pocos de potenciais possam ser construidas. Nesse trabalho estudamos o poco duplo quadrado unidimensional assimetrico que possui potencial para uma variedade de aplicacoes, por exemplo, o aprisionamento atomico devido a diferenca de profundidades entre pocos vizinhos. As funcoes de onda e autovalores de energia sao determinados explicitamente para um caso ressonante e outro nao ressonante.

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R. M. Ricotta

Papers

Supersymmetry, variational method and hulthen potential

Supersymmetric variational energies of 3d confined potentials

Variational supersymmetric approach to evaluate Fokker–Planck probability

Hamiltonian hierarchy of pseudo-potentials

Solução quântica para o poço duplo quadrado unidimensional assimétrico