An alternative series solution to the isotropic quartic oscillator in N dimensions

The series solution of the N-dimensional isotropic quartic oscillator weighted by an appropriate function which exhibits the correct asymptotic behavior of the wave function is presented. The numerical performance of the solution in Bill's determinant picture is excellent, and yields the energy spectrum of the system to any desired accuracy for the full range of the coupling constant. Furthermore, it converges to the well-known exact solution of the unperturbed harmonic oscillator wave function, when the anharmonic interaction vanishes.


Türker, Burhan Lemi (Springer Science and Business Media LLC, 1992-01-01)
A novel method, based on the topology of the cardinal vertex, is described to find an upper bound for the largest eigenvalue of a graph.
Exact solutions of the Schrodinger equation via Laplace transform approach: pseudoharmonic potential and Mie-type potentials
Arda, Altug; Sever, Ramazan (Springer Science and Business Media LLC, 2012-04-01)
Exact bound state solutions and corresponding normalized eigenfunctions of the radial Schrodinger equation are studied for the pseudoharmonic and Mie-type potentials by using the Laplace transform approach. The analytical results are obtained and seen that they are the same with the ones obtained before. The energy eigenvalues of the inverse square plus square potential and three-dimensional harmonic oscillator are given as special cases. It is shown the variation of the first six normalized wave-functions ...
A class of orthogonal polynomials suggested by a trigonometric Hamiltonian : Symmetric states
Taşeli, Hasan (Springer Science and Business Media LLC, 2004-05-01)
A new subclass of the Jacobi polynomials arising in the exact analytical solution of the one-dimensional Schrodinger equation with a trigonometric potential has been introduced. The polynomials which consist of a free parameter are not ultraspherical polynomials and have been simply named the T - polynomials since they are generated by a trigonometric Hamiltonian. In certain sense, it is shown that the T - polynomials can be regarded as a generalisation of the airfoil polynomials or the Chebyshev polynomial...
The Laguerre pseudospectral method for the reflection symmetric Hamiltonians on the real line
Taşeli, Hasan (Springer Science and Business Media LLC, 2007-05-01)
Hermite-Weber functions provide a natural expansion basis for the numerical treatment of the Schrodinger equation on the whole real line. For the reflection symmetric Hamiltonians, however, it is shown here that the transformation of the problem over the half line and use of a Laguerre basis is computationally much more efficient in a pseudospectral scheme.
A formula for the joint local spectral radius
Emel'yanov, EY; Ercan, Z (American Mathematical Society (AMS), 2004-01-01)
We give a formula for the joint local spectral radius of a bounded subset of bounded linear operators on a Banach space X in terms of the dual of X.
Citation Formats
H. Taşeli, “An alternative series solution to the isotropic quartic oscillator in N dimensions,” JOURNAL OF MATHEMATICAL CHEMISTRY, pp. 235–245, 1996, Accessed: 00, 2020. [Online]. Available: