A Hill-series approach to wavefunction nodes

The Hill-series method is shown to have several advantages for treating the Schrödinger equation when the wavefunction obeys the Dirichlet boundary condition Ψ(R) = 0. A novel combination of the virial theorem, the Hill-series method and a finite difference method is used to find the node positions of the wavefunction for several excited states of perturbed oscillator and coulombic systems and to find critical radii for the hydrogen atom.

[1]  K. Sen,et al.  Simultaneous degeneracy of the confined 2D hydrogen atom energy levels , 2008 .

[2]  D. Baye,et al.  Confined hydrogen atom by the Lagrange-mesh method: energies, mean radii, and dynamic polarizabilities. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  F. Fern'andez.  New approach to separable bounded quantum-mechanical models , 2008, 0805.3152.

[4]  F. Fernández.  The accurate calculation of resonances in multiple-well oscillators , 2007, 0711.2289.

[5]  H. Ciftci,et al.  Study of a bounded oscillator problem in one dimension , 2007 .

[6]  J. Killingbeck.  A Hill-series method for resonances , 2007 .

[7]  A. Hyder,et al.  Green's operator for Hamiltonians with Coulomb plus polynomial potentials , 2006, math-ph/0612053.

[8]  F. Fernández,et al.  Alternative perturbation expansions for partially solvable quantum-mechanical models , 2006 .

[9]  A. J. Zakrzewski,et al.  Highly precise solutions of the one-dimensional Schrödinger equation with an arbitrary potential , 2006, Comput. Phys. Commun..

[10]  P. Kościk,et al.  Application of the frobenius method to the schrodinger equation for a spherically symmetric potential : an anharmonic oscillator , 2005, quant-ph/0512087.

[11]  H. Alhendi,et al.  High-Precision Numerical Determination of Eigenvalues for a Double-Well Potential Related to the Zinn-Justin Conjecture , 2004, quant-ph/0402101.

[12]  G. Campoy,et al.  Accurate energy eigenvalues and eigenfunctions for the two‐dimensional confined hydrogen atom , 2005 .

[13]  A. Nanayakkara.  Zeros of the wave functions of general polynomial potentials , 2004 .

[14]  B. Burrows,et al.  A hydrogen-like atom confined within an impenetrable spherical box , 2002 .

[15]  Y. P. Varshni.  Critical cage radii for a confined hydrogen atom , 1998 .

[16]  F. Fernández.  Accurate treatment of simple models for self-interaction , 1997 .

[17]  N. Aquino.  The isotropic bounded oscillators , 1997 .

[18]  J. Killingbeck.  The exponential cosine screened potential , 1988 .

[19]  J. Killingbeck.  Hill determinants and 1/N theory , 1985 .

[20]  J. Killingbeck.  Direct expectation value calculations , 1985 .

[21]  E. Castro,et al.  Hypervirial analysis of enclosed quantum mechanical systems. I. Dirichlet boundary conditions , 1981 .

[22]  K. Banerjee,et al.  Two-well oscillator , 1978 .

[23]  J. Killingbeck.  A pocket calculator determination of energy eigenvalues , 1977 .