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  1. 2 Open Physics

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  1. 1 2014

  2. 1 2013

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  1. 1 Brandon D.

  2. 1 Iacob F.

  3. 1 Saad N.

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Spectral characterization of hydrogen-like atoms confined by oscillating systems

100%
Iacob F.
Open Physics
|
2014
|
vol. 12
|
issue 9
628-636
EN
The spectral characterization of Coulomb systems confined by a homogeneous pseudo-Gaussian oscillator is investigated. This is done using the efficient computational method of generating functionals. Also, this method is used for the spectral characterization of homogeneous harmonic oscillator confinement, treated as a particular case of pseudo-Gaussian oscillator confinement. Finally, confinement by an impenetrable sphere of finite radius is considered by studying its conjugate effect along with a harmonic oscillator.
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Exact and approximate solutions to Schrödinger’s equation with decatic potentials

75%
Brandon D., Saad N.
Open Physics
|
2013
|
vol. 11
|
issue 3
279-290
EN
The one-dimensional Schrödinger’s equation is analysed with regard to the existence of exact solutions for decatic polynomial potentials. Under certain conditions on the potential’s parameters, we show that the decatic polynomial potential V (x) = ax 10 + bx 8 + cx 6 + dx 4 + ex 2, a > 0 is exactly solvable. By examining the polynomial solutions of certain linear differential equations with polynomial coefficients, the necessary and sufficient conditions for corresponding energy-dependent polynomial solutions are given in detail. It is also shown that these polynomials satisfy a four-term recurrence relation, whose real roots are the exact energy eigenvalues. Further, it is shown that these polynomials generate the eigenfunction solutions of the corresponding Schrödinger equation. Further analysis for arbitrary values of the potential parameters using the asymptotic iteration method is also presented.
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