SUSY SUPERPOTENTIALS FOR A CONFINED HULTHÉN POTENTIAL

A system consisting of an ion and an electron interacting through the Hulthén potential confined in an impenetrable spherical box, with the ion at the centre is considered. Superpotential which is the crucial quantity in supersymmetric quantum mechanics is proposed for the 1s and 2p states. Variational wave functions are thence derived. Energies are calculated from these for different values of the radius of box (R) and these are compared to the exact values; good agreement is shown to exist between the two. The variational wave functions are further employed to calculate the absorption oscillator strength for the 1s→2p transition and the dipole polarizability for different values of R.

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Wave functions for the hydrogen atom in a dense plasma

Canadian Journal of Physics ◽

10.1139/p03-098 ◽

2003 ◽

Vol 81 (11) ◽

pp. 1243-1248 ◽

Cited By ~ 1

Author(s):

Y P Varshni

Keyword(s):

Hydrogen Atom ◽

Dense Plasma ◽

Wave Functions ◽

Electron Interaction ◽

Dipole Polarizability ◽

Variational Wave Functions ◽

Absorption Oscillator Strength ◽

Variational Wave ◽

Good Agreement ◽

03.65 Ge

A hydrogen atom in a high-density plasma is simulated by a model in which the hydrogen atom is confined in an impenetrable spherical box, with the atom at the centre. For the protonelectron interaction the DebyeHuckel potential is used. Variational wave functions are proposed for the 1s and 2p states. Energies calculated from these for different values of the radius of box (r0) are shown to be in good agreement with the exact values. The variational wave functions are further employed to calculate the absorption oscillator strength for the 1s [Formula: see text] 2p transition and the dipole polarizability for different values of r0. PACS Nos.: 03.65.Ge, 32.70.Os, 31.70.Dk, 52.20.j

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On the computation of dipole transitions in the HD molecule. Part II

Canadian Journal of Physics ◽

10.1139/p76-075 ◽

1976 ◽

Vol 54 (6) ◽

pp. 672-679 ◽

Cited By ~ 58

Author(s):

L. Wolniewicz

Keyword(s):

Ground State ◽

Wave Functions ◽

Nonadiabatic Coupling ◽

Transition Moments ◽

The Mean ◽

Variational Wave Functions ◽

Theoretical Results ◽

Variational Wave ◽

Electronic Ground ◽

Good Agreement

The nonadiabatic coupling with Πu states in the electronic ground state of the HD molecule is discussed. Formulas are given that facilitate the evaluation of Πu contributions to the energies and transition moments. Numerical computations are performed for all ν ≤ 4 vibrational and J ≤ 4 rotational levels yielding the Πu and Σu nonadiabatic corrections. The variational wave functions are employed to compute the transition moments for the 0–ν bands with ν ≤ 4. The results are in good agreement with experimental data except in the case of the 0–ν band where the theoretical results are larger than the mean experimental moment by a factor of about 1.4.

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NONLINEAR MOBILITY IN A SUPERCONDUCTING TUNNEL JUNCTION INVOLVING VARIATIONAL WAVE FUNCTIONS

Modern Physics Letters B ◽

10.1142/s0217984994001308 ◽

1994 ◽

Vol 08 (21n22) ◽

pp. 1343-1352

Author(s):

A. EXTREMERA

Keyword(s):

Tunnel Junction ◽

Variational Approach ◽

Current Model ◽

Decay Rates ◽

Wave Functions ◽

Superconducting Tunnel Junction ◽

Ferroelectric Capacitor ◽

Variational Wave Functions ◽

Variational Wave ◽

Good Agreement

We consider the effect of dissipation on the nonlinear mobility in a superconducting tunnel junction. Using a variational approach, the critical mobility crucially depends on the coupling to the ohmic bath. At ultrasmall capacitances, good agreement is found with decay rates diagrams. The current model could be developed in other contexts, such as that of a ferroelectric capacitor, as proposed by Widom and Clark (Phys. Rev.B30, 1205 (1984)).

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Analytical bound-state solutions of the Schrödinger equation for the Manning–Rosen plus Hulthén potential within SUSY quantum mechanics

International Journal of Modern Physics A ◽

10.1142/s0217751x18500215 ◽

2018 ◽

Vol 33 (03) ◽

pp. 1850021 ◽

Cited By ~ 5

Author(s):

A. I. Ahmadov ◽

Maria Naeem ◽

M. V. Qocayeva ◽

V. A. Tarverdiyeva

Keyword(s):

Quantum Mechanics ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Jacobi Polynomials ◽

Bound State ◽

Wave Functions ◽

Hulthén Potential ◽

Radial Wave ◽

Energy Eigenvalues ◽

Hulthen Potential

In this paper, the bound-state solution of the modified radial Schrödinger equation is obtained for the Manning–Rosen plus Hulthén potential by using new developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial wave functions are defined for any [Formula: see text] angular momentum case via the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. Thanks to both methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is presented. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary [Formula: see text] states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to [Formula: see text] radial and [Formula: see text] orbital quantum numbers.

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The bound state solutions of the D-dimensional Schrödinger equation for the Hulthén potential within SUSY quantum mechanics

International Journal of Modern Physics E ◽

10.1142/s0218301317500288 ◽

2017 ◽

Vol 26 (05) ◽

pp. 1750028 ◽

Cited By ~ 7

Author(s):

H. I. Ahmadov ◽

M. V. Qocayeva ◽

N. Sh. Huseynova

Keyword(s):

Quantum Mechanics ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Dimensional Space ◽

Energy Levels ◽

Wave Functions ◽

Hulthén Potential ◽

Radial Wave ◽

Energy Eigenvalues ◽

Hulthen Potential

In this paper, the analytical solutions of the [Formula: see text]-dimensional hyper-radial Schrödinger equation are studied in great detail for the Hulthén potential. Within the framework, a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any [Formula: see text] orbital angular momentum case within the context of the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transforming each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary [Formula: see text] states for [Formula: see text]-dimensional space.

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