The scaled Hermite-Weber basis still highly competitive

The effectiveness of the usual harmonic oscillator basis is demonstrated on a wide class of Schrodinger Hamiltonians with various spectral properties. More specifically, it is shown numerically that an appropriately scaled Hermite-Weber basis yields extremely accurate results not only for the energy eigenvalues which differ slighly from the harmonic oscillator levels, but also for the states which reflect a purely anharmonic character.


An alternative series solution to the isotropic quartic oscillator in N dimensions
Taşeli, Hasan (Springer Science and Business Media LLC, 1996-01-01)
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 an...
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.
Supersymmetric solutions of PT-/non-PT-symmetric and non-Hermitian screened Coulomb potential via Hamiltonian hierarchy inspired variational method
Faridfathi, Gholamreza; Sever, Ramazan (Springer Science and Business Media LLC, 2007-10-01)
The supersymmetric solutions of PT -symmetric and Hermitian/non-Hermitian forms of quantum systems are obtained by solving the Schrodinger equation for the Exponential-Cosine Screened Coulomb potential. The Hamiltonian hierarchy inspired variational method is used to obtain the approximate energy eigenvalues and corresponding wave functions.
A finite element variational multiscale method for the Navier-Stokes equations
Volker, John; Kaya Merdan, Songül (Society for Industrial & Applied Mathematics (SIAM), 2005-01-01)
This paper presents a variational multiscale method (VMS) for the incompressible Navier-Stokes equations which is defined by a large scale space L-H for the velocity deformation tensor and a turbulent viscosity nu(T). The connection of this method to the standard formulation of a VMS is explained. The conditions on L-H under which the VMS can be implemented easily and efficiently into an existing finite element code for solving the Navier - Stokes equations are studied. Numerical tests with the Smagorinsky ...
Modified l-states of diatomic molecules subject to central potentials plus an angle-dependent potential
Berkdemir, Cueneyt; Sever, Ramazan (Springer Science and Business Media LLC, 2009-11-01)
We present modified a""-states of diatomic molecules by solving the radial and angle-dependent parts of the Schrodinger equation for central potentials, such as Morse and Kratzer, plus an exactly solvable angle-dependent potential V (theta) (theta)/r (2) within the framework of the Nikiforov-Uvarov (NU) method. We emphasize that the contribution which comes from the solution of the Schrodinger equation for the angle-dependent potential modifies the usual angular momentum quantum number a"". We calculate exp...
Citation Formats
H. Taşeli, “The scaled Hermite-Weber basis still highly competitive,” JOURNAL OF MATHEMATICAL CHEMISTRY, pp. 177–187, 2003, Accessed: 00, 2020. [Online]. Available: