Fortran 90 procedures for computing matrix elements associated to the scaled Pöschl-Teller potential

The PDF file attached to this document contents all routines needed for computation of  matrix elements associated to the scaled Pöschl-Teller potentiel given by -U0sech^2(α*x*exp(θ*i)). This computation is based on the spectral Galerkin method using Pöschl-Teller sturmian functions as basis functions. To calculate the matrix elements in question, one simply has to put the following instruction in the main program or the calling procedure: call scaledptl(nsturm,theta,U0,mat_U)

Note that nsturm, theta and U0 are input arguments. The module named nrtype must contain two parameters dp (for double precision) and qp (for quadruple precision). morescaled_PTP-matrx

A FORTRAN90 code to compute energies and wave-functions for the V0cosh^2(µ)[tanh((x-µd)/d)+tanh(µ)]^2 potential

The code presented calculates energies and normalized wave-functions associated with a simple system consisting of an electron trapped in a one-dimensional potential defined by the equation V0cosh^2(µ)[tanh(x-µd)/d+tanh(µ)]^2 where V0, µ and d are positive real parameters, whereas  x belongs to R. The time-independent Schrödinger equation is solved by means of the Galerkin method consisting of developing the wavefunction on a finite basis of sturmian functions associated with the Pöschl-Teller potential. The entire code is contained in a compressed file named nyengeri-david-code-real-2015-01.pdf.

The compressed file nyengeri-david-code-complex-2015-01.pdf concerns a complex version of our code which can be used to illustrate the Aguilar, Balslev, Combes and Simon’s theorem. moreattached-documents

Un code FORTRAN95 pour calculer la structure spectrale du modèle atomique de Rosen-Morse

Le présent code sert à calculer numériquement les énergies et fonctions propres du modèle atomique de Rosen-Morse. La méthode numérique utilisée est la méthode spectrale de Galerkin. Celle-ci consiste à développer la fonction d’onde sur une base finie de fonctions sturmiennes appropriées. Le code tout entier est contenu dans le fichier compressé   Rosen-Morse-code-2012-03-14.pdf.  Le fonctionnement du code est décrit dans le programme principal RM-code.f95. more

The Kullback-Leibler Number and Thermodynamics

In this article, we establish a connection between the Kullback-Liebler number and thermodynamics in using the canonical ensemble thermodynamic probability in the most probable distribution. As a result, we obtain many expressions, each connecting the Kullback-Leibler number to one, two or many of the following thermodynamic quantities: the canonical ensemble partition function, the entropy of the canonical ensemble in the most probable distribution, the canonical ensemble average of energy, the Helmholz free energy, the standard deviation in the energy of the canonical ensemble, the heat capacity at constant volume, the absolute temperature T and the temperature parameter .

more KLN_thermodynamics

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