Corrêa Silva, E. V.; Monerat, G. A.; de Oliveira Neto, G.; Ferreira Filho, L. G. Spectral: solving schroedinger and Wheeler-dewitt equations in the positive semi-axis by the spectral method. (English) Zbl 1344.35002 Comput. Phys. Commun. 185, No. 1, 380-391 (2014). Summary: The Galerkin spectral method can be used for approximate calculation of eigenvalues and eigenfunctions of unidimensional Schroedinger-like equations such as the Wheeler-DeWitt equation. The criteria most commonly employed for checking the accuracy of results is the conservation of norm of the wave function, but some other criteria might be used, such as the orthogonality of eigenfunctions and the variation of the spectrum with varying computational parameters, e.g. the number of basis functions used in the approximation. The package Spectra, which implements the spectral method in Maple language together with a number of testing tools, is presented. Alternatively, Maple may interact with the Octave numerical system without the need of Octave programming by the user. Cited in 3 Documents MSC: 35-04 Software, source code, etc. for problems pertaining to partial differential equations 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 35Q41 Time-dependent Schrödinger equations and Dirac equations 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics Keywords:Schroedinger-like equation; Wheeler-deWitt equation; Galerkin spectral method Software:Spectral; Spectra; Maple; Octave PDFBibTeX XMLCite \textit{E. V. Corrêa Silva} et al., Comput. Phys. Commun. 185, No. 1, 380--391 (2014; Zbl 1344.35002) Full Text: DOI References: [1] DeWitt, B. S., Phys. Rev., 160, 1113 (1967) · Zbl 0158.46504 [2] Schutz, B. F., Phys. Rev. D, 2, 2762 (1970) [3] Schutz, B. F., Phys. Rev. D, 4, 3559 (1971) [4] Lapchinskii, V. G.; Rubakov, V. A., Theoret. Math. Phys., 33, 1076 (1977) [5] Lemos, N. A., J. Math. Phys., 37, 1449 (1996) · Zbl 0865.58062 [6] Gotay, M. J.; Demaret, J., Phys. Rev. D, 28, 2402 (1983) [7] Alvarenga, F. G.; Fabris, J. C.; Lemos, N. A.; Monerat, G. A., Gen. Relativity Gravitation, 34, 651 (2002) · Zbl 0998.83076 [8] Pedram, P., Gen. Relativity Gravitation, 40, 1663 (2008) · Zbl 1145.83370 [9] Pedram, P.; Mirzaei, M.; Gousheh, S. S., Comput. Phys. Commun., 176, 581 (2007) · Zbl 1196.65178 [10] Barboza, E. M.; Lemos, N. A., Gen. Relativity Gravitation, 38, 1609 (2006) · Zbl 1117.83040 [11] Oliveira Neto, G.; Monerat, G. A.; Corrêa Silva, E. V.; Neves, C.; Ferreira Filho, L. G., Int. J. Mod. Phys.: Conference Series, 3, 254 (2011) [12] Monerat, G. A.; Oliveira-Neto, G.; Corrêa Silva, E. V.; Ferreira-Filho, L. G.; Romildo, P.; Fabris, J. C.; Fracalossi, R.; Gonçalves, S. V.B.; Alvarenga, F. G., Phys. Rev. D, 76, 024017 (2007) [13] Monerat, G. A.; Ferreira-Filho, L. G.; Oliveira-Neto, G.; Corrêa Silva, E. V.; Neves, C., Phys. Lett. A, 374, 4741 (2010) · Zbl 1238.83082 [14] Boyd, J. P., Chebyshev and Fourier Spectral Methods (2001), Dover: Dover New York · Zbl 0994.65128 [16] Sagan, H., Boundary and Eigenvalue Problems in Mathematical Physics (1989), Dover: Dover New York · Zbl 1227.35003 [17] Dirac, P. A.M., The Principles of Quantum Mechanics (1967), Clarendon Press: Clarendon Press Oxford · JFM 56.0745.05 [21] Merzbacher, E., Quantum Mechanics (1998), John Willey & Sons: John Willey & Sons New York This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.