Density functional studies on the hollow resonances in the Li-isoelectronic sequence ( Z = 4–10)

2014

Mod. Phys. Lett. A

Accurate ro-vibrational energies, eigenfunctions, radial densities, expectation values are presented for the exponential-type Manning-Rosen (MR) potential. Bound states accurate up to ten significant figure are obtained by employing a simple, reliable generalized pseudospectral method.All 55 eigenstates with n ≤ 10 are treated for arbitrary values of potential parameters, covering a wide range of interaction, through a non-uniform, optimal spatial radial discretization. A detailed investigation has been made on energy changes with respect to screening and other potential parameters. A systematic estimation of critical screening parameters are given for these eigenstates.Special emphasis has been given to higher states and in the vicinity of critical screening region.A thorough comparison with literature results is made wherever possible. This surpasses the accuracy of all other existing methods currently available. Several new states are reported for the first time. In short, a simple, efficient scheme for accurate calculation of this and other molecular potentials is offered. notable approaches are: a super-symmetric shape invariance formalism in conjunction with function analysis method [11], an approximation for centrifugal term different from the usual one used above, containing 3 adjustable parameters in it [12], yet another alternative approximation to the centrifugal potential within a Nikiforov-Uvarov method [13], the Duru-Kleinert method of path-integral formalism [14], Laguerre and oscillator bases to tridiagonalize the reference Hamiltonian and subsequently a Gauss quadrature approach for

Section: Gps Methods For Mr Potentialmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Studies on bound-state spectra of Manning–Rosen potential

2014

Mod. Phys. Lett. A

“…The GPS method has been found to be very successful for various physical and chemical systems as evidenced by the following applications [27,[38][39][40][41][42][43]. Therefore here we highlight only the essential aspects.…”

Section: Methods Of Calculationmentioning

confidence: 99%

“…Some of these are spiked harmonic oscillator, Hulthén, Yukawa, logarithmic, rational, power-law potentials, ro-vibrational levels in molecules as well as ground and Rydberg states in atoms, etc. [27,[38][39][40][41][42][43]. Only in [27], however, this was employed for confined quantum states.…”

Section: Introductionmentioning

confidence: 99%

Confinement in 3D polynomial oscillators through a generalized pseudospectral method

2014

Mod. Phys. Lett. A

“…Moreover, in order to understand the spectra, we make a detailed analysis on the effect of variation of the parameters on eigenvalues and radial densities. For this we employ the GPS method, which has been very successful to produce accurate and reliable results in recent years for a variety of singular potentials relevant to quantum mechanics, static and dynamic properties of atom, molecules, as well as the spherically confined isotropic harmonic oscillator [18,[25][26][27][28]. The article is organized as follows: Section II gives a brief outline of the GPS method used here to solve the SE for the GSHO.…”

Section: Introductionmentioning

confidence: 99%

Bound states of the generalized spiked harmonic oscillator

Journal of Molecular Structure: THEOCHEM

Jalbout

2008

Bound states of the generalized spiked harmonic oscillator potential are calculated accurately by using the generalized pseudospectral method. Energy eigenvalues, various expectation values, radial densities are obtained through a nonuniform, optimal spatial discretization of the radial Schrödinger equation efficiently. Ground and excited states corresponding to arbitrary values of n and ℓ are reported for potential parameters covering a wide range of interaction. Both weak and strong coupling is considered. The effect of potential parameters on eigenvalues and densities are discussed. Almost all of the results are reported here for the first time, which could be useful for future studies.The spiked harmonic oscillator (SHO) defined by the Hamiltonian H = −d 2 /dr 2 + r 2 + λr −α , where r ∈ [0, ∞] and λ, α are positive definite parameters signifying the strength of perturbation and type of singularity, has been of considerable interest for over three decades. This has a number of interesting physical as well as mathematical properties and found applications in chemical, nuclear and particle physics. For example, this represents a prototype of the so-called Klauder phenomenon [1, 2], i.e., even after the perturbation is completely turned off (λ → 0), some interaction still remains. The Rayleigh-Schrödinger perturbation series diverges following the relation n ≥ 1/(α − 2), with n denoting the order of perturbation. Another interesting feature is that in the region of α ≥ 5/2, this gives rise to supersingularity, i.e., the potential is so singular that any nontrivial correction to the energy (matrix element) diverges [1]. A fascinating property from a purely mathematical point of view is that there is no dominance of either of the two terms r 2 and λ/r α for the extreme values of λ. In other words, there is a tug-of-war between the two terms. Typical shape of the potential for a few parameter sets are depicted in Fig. 1 Like most of the practical physical systems, exact analytical solution of the corresponding Schrödinger equation (SE) for arbitrary parameters for a general state (both ground and excited) is yet to be known and consequently approximations such as variational or perturbation methods must be used. Thus a large number of attempts have been made towards the exact and approximate calculation of eigenvalues and eigenfunctions employing analytic, seminumerical or purely computational methods [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. As the Rayleigh-Schrödinger perturbation series for the eigenvalues of the operator H diverges [3], a modified perturbation theory to finite order was developed which gave good result for the ground-state eigenvalues of small λ. For large positive values of λ, approximate estimates were made through the large coupling perturbative expansion [3]. A resummation technique for weak coupling of the nonsingular SHO (α < 5/2) [4] was developed. Exact and approximate solutions are also given for the lowest states of a given angular momentum [6]. A WKB treatment has be...