On the exact solution of the Schrodinger equation with a quartic anharmonicity

A new version of solutions in the form of an exponentially weighted power series is constructed for the two-dimensional circularly symmetric quartic oscillators, which reflects successfully the desired properties of the exact wave function. The regular series part is shown to be the solution of a transformed equation. The transformed equation is applicable to the one-dimensional problem as well. Moreover, the exact closed-form eigenfunctions of the harmonic oscillator can be reproduced as a special case of the present wave function. (C) 1996 John Wiley & Sons, Inc.


Tezer, Münevver (Informa UK Limited, 1990-01-01)
An oscillating infinite series involving product of Bessel function J o(x) and an oscillating infinite series involving trigonometric function sin(x) were evaluated and computed numerically in [1] and [2] respectively. In this paper, an oscillating infinite series involving product of exponential, Bessel and trigonometric functions is evaluated. The series is transformed first into the sum of two infinite integrals by using contour integration and then the infinite integral with oscillating integrand is tra...
On the deformation chirality of real cubic fourfolds
Finashin, Sergey (Wiley, 2009-09-01)
According to our previous results, the conjugacy class of the involution induced by the complex conjugation in the homology of a real non-singular cubic fourfold determines the fourfold tip to projective equivalence and deformation. Here, we show how to eliminate the projective equivalence and obtain a pure deformation classification, that is, how to respond to the chirality problem: which cubics are not deformation equivalent to their image under a mirror reflection. We provide an arithmetical criterion of...
On the Poisson sum formula for the analysis of wave radiation and scattering from large finite arrays
Aydın Çivi, Hatice Özlem; Chou, HT (1999-05-01)
Poisson sum formulas have been previously presented and utilized in the literature [1]-[8] for converting a finite element-by-element array field summation into an alternative representation that exhibits improved convergence properties with a view toward more efficiently analyzing wave radiation/scattering from electrically large finite periodic arrays. However, different authors [1]-[6] appear to use two different versions of the Poisson sum formula; one of these explicitly shows the end-point discontinui...
An alternative simple solution of the sextic anharmonic oscillator and perturbed coulomb problems
IKHDAİR, SAMEER; Sever, Ramazan (World Scientific Pub Co Pte Lt, 2007-10-01)
Utilizing an appropriate ansatz to the wave function, we reproduce the exact bound-state solutions of the radial Schrodinger equation to various exactly solvable sextic an-harmonic oscillator and confining perturbed Coulomb models in D-dimensions. We show that the perturbed Coulomb problem with eigenvalue E can be transformed to a sextic anharmonic oscillator problem with eigenvalue P. We also check the explicit relevance of these two related problems in higher-space dimensions. It is shown that exact solut...
On the Poisson sum formula for analysis of EM radiation/scattering from large finite arrays
Aydın Çivi, Hatice Özlem; Chou, HT (1998-01-01)
A useful procedure, that has been described previously in the literature, employs the Poisson sum formula to represent the solution to the fields of a three-dimensional (3D) large periodically spaced finite planar array problem configuration as a convolution of the infinite planar periodic array solution and the Fourier transform of the equivalent aperture distribution over the finite array. It is shown here that the Poisson sum formula utilized by Felsen and Carin (see J. Opt. Soc. Am. A, vol.11, no.4, p.1...
Citation Formats
H. Taşeli, “On the exact solution of the Schrodinger equation with a quartic anharmonicity,” INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, pp. 63–71, 1996, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/53579.