Hydrogen atom in ellipsoidal cavity

Kang, Shimin; Liu, Qiang; Meng, Hao; Shi, Tao

doi:10.1016/j.physleta.2006.08.055

Cited by 26 publications

(27 citation statements)

References 45 publications

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“…the azimuthal quantum number defining the σ,π,δ,… states and ψ(ξ,η) that part of the total wavefunction which now has to be constructed through use of approximate methods. This aspect was originally pointed out by Kang et al 37 in their study of the hydrogen atom confined by a spheroidal cavity.…”

Section: Theorymentioning

confidence: 80%

“…As in the previous cases, we first compare the predictions of this work using the ansatz wavefunction given by Eq. (11c) with corresponding exact 33 and approximate 35–37 calculations available in the literature for H with its nucleus fixed at one of the foci. Table VI shows the energy values obtained here for the 1sσ state of H confined by a hard prolate spheroid characterized by an interfocal distance D = 2 a.u.…”

Section: Resultsmentioning

confidence: 99%

“…A common feature appearing in all these studies is the use of prolate spheroidal coordinates where the nuclear positions are clamped at the foci of the confining spheroidal cavity. Furthermore, the hydrogen atom enclosed by a prolate spheroidal cavity has been also studied on the same footing 32, 33, 35, 36, except for a recent report by Kang et al 37, who use the linear variation method and B‐spline expansions for the wavefunction to analyze the more general situation whereby the atom nuclear position is located out of the foci.…”

Section: Introductionmentioning

confidence: 99%

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Development and characterization of homogeneous membranes prepared from sulfonated poly(phenylene oxide)

Guan

Gong

et al. 2005

J of Applied Polymer Sci

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This article investigates the comprehensive properties of sulfonated poly(phenylene oxide) (SPPO) membranes with different sulfonation degrees and presents the completion of previous work necessary for the application of SPPO membranes to proton-exchange membrane fuel cells. The sulfonation level has been accurately determined by conductometric titration and 1 H-NMR, and the glasstransition temperature has been obtained with both differential scanning calorimetry and dynamic mechanical thermal analysis. Sulfonic groups attached to the aromatic ring in the poly(phenylene oxide) backbone split at 220 -340°C, but the main-chain splitting temperature of SPPO is similar to that of the pure polymer. In addition, the effects of sulfonic groups and water on the tensile strength of these membranes have been studied. An increase in the sulfonate groups in the polymer results in an increase in the water uptake. Atomic force microscopy phase images of the acidform membranes clearly show the hydrophilic domains, and the ionic regions of the membranes with a low sulfonation degree are isolated and become connected to produce a cocontinuous morphology as the degree of sulfonation increases.

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Section: Theorymentioning

confidence: 80%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Development and characterization of homogeneous membranes prepared from sulfonated poly(phenylene oxide)

Guan

Gong

et al. 2005

J of Applied Polymer Sci

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“…Sommerfeld et al car-ried out investigations into the energy levels of hydrogen in a spherical box [34]. Since then a number of calculations have been performed for studying the energy levels of confined atoms [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]. During the last 80 years this model has been proved to be quite useful in the theories of liquids, high-pressure physics, and many other fields, including the effect of pressure on energy levels, polarizabilities and ionization potentials of atoms and molecules, the cell model of the liquid state and semiconductor quantum dots.…”

Section: Introductionmentioning

confidence: 99%

“…The B-spline method can be found in the Refs [52][53][54]. A number of theoretical investigations on atomic systems based on Bspline basis functions have been reported [48][49][50][51][52][53][54][55][56][57][58][59][60]. Very recently, Lin et al have reported the spectral data of helium atoms with screened Coulomb potentials using this approach [60].…”

Section: Introductionmentioning

confidence: 99%

The hydrogen atom confined in both Debye screening potential and impenetrable spherical box

Kang¹,

Yang

et al. 2013

Open Physics

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Abstract:The ground state energy, some low-lying excited state energies and oscillator strengths for a hydrogen atom confined in both a Debye screening potential and finite impenetrable spherical box have been calculated. These have been calculated using a linear variational method based on B-spline basis functions. The results have been compared with those of other authors. The evaluated energies and oscillator strengths with respect to different plasma screening parameters with a certain confinement radii are discussed. PACS

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Spheroidal confinement of a single electron and of the hydrogen atom, the H and HeH⁺⁺ molecular ions with arbitrary nuclear positions along the major axis

Cruz

Colín-Rodríguez

2009

Int J of Quantum Chemistry

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ABSTRACT:Evidence is given on the usefulness of the variational method to explore the nonseparable Schroedinger problem for the energy evolution of one-electron atoms and diatomic molecular ions confined by a hard prolate spheroidal cavity when the nuclear positions do not coincide with the foci. In this work, we study explicity the case of the hydrogen atom (H) and the H 2 ϩ and HeH ϩϩ under the aforementioned confinement conditions and obtain variationally the energy evolution as a function of nuclear positions along the major axis of a confining spheroid of fixed size and eccentricity. The particular case of an electron (e Ϫ ) under the same confinement conditions is also addressed using the same methodology. Our calculations are restricted to the ground states of H (1s), HeH ϩϩ (1s), e Ϫ ͑1s͒ and the ground-state ͑1s g ) and first excited state (2p u ) of H 2 ϩ . It is shown that a simple LCAO Dickinsontype variational ansatz wavefunction adapted for the confinement case of all systems treated in this work provides very rewarding results for the energy dependence on the size and shape of the confining cavity when compared with corresponding available exact calculations. For e Ϫ as well as for H, H 2 ϩ and HeH ϩϩ with "on-focus" nuclear positions excellent general quantitative agreement is observed. For the "off-focus" case, moderate quantitative agreement is obtained with available accurate B-spline variational calculations for H. For the molecular systems with "off-focus" nuclear positions, the results of this work are the first of this kind.

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Hydrogen atom in ellipsoidal cavity

Cited by 26 publications

References 45 publications

Development and characterization of homogeneous membranes prepared from sulfonated poly(phenylene oxide)

Development and characterization of homogeneous membranes prepared from sulfonated poly(phenylene oxide)

The hydrogen atom confined in both Debye screening potential and impenetrable spherical box

Spheroidal confinement of a single electron and of the hydrogen atom, the H and HeH⁺⁺ molecular ions with arbitrary nuclear positions along the major axis

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Hydrogen atom in ellipsoidal cavity

Cited by 26 publications

References 45 publications

Development and characterization of homogeneous membranes prepared from sulfonated poly(phenylene oxide)

Development and characterization of homogeneous membranes prepared from sulfonated poly(phenylene oxide)

The hydrogen atom confined in both Debye screening potential and impenetrable spherical box

Spheroidal confinement of a single electron and of the hydrogen atom, the H and HeH++ molecular ions with arbitrary nuclear positions along the major axis

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Product

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Spheroidal confinement of a single electron and of the hydrogen atom, the H and HeH⁺⁺ molecular ions with arbitrary nuclear positions along the major axis