Degeneracy of energy levels of pseudo-Gaussian oscillators

Lute

Annals of West University of Timisoara - Physics

2015

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The Schrödinger equation with pseudo-Gaussian potential is investigated. The pseudo-Gaussian potential can be written as an infinite power series. Technically, by an ansatz to the wave-functions, exact solutions can be found by analytic approach [12]. However, to calculate the solutions for each state, a condition that will stop the series has to be introduced. In this way the calculated energy values may suffer modifications by imposing the convergence of series. Our presentation, based on numerical methods, is to compare the results with those obtained in the analytic case and to determine if the results are stable under different stopping conditions.

Section: Computing Methods and Resultssupporting

confidence: 60%

Section: Introductionmentioning

confidence: 99%

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A Numerical Approach for the Solution of Schrödinger Equation With Pseudo-Gaussian Potentials

Lute

Annals of West University of Timisoara - Physics

2015

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“…The potential (1) with terms grouped as in (7), allows us to recognize that it is basically made up by a term representing the HO potential V HO = λ+r 2 , with λ an arbitrary energy level and an additional term, which is actually a power series, V int = k=s+1Ĉ n r 2k .…”

Section: The Physical Modelmentioning

confidence: 99%

“…The exact solution of Schrödinger equation for the pseudo-Gaussian potential was presented in [7]. It was found that this potential belongs to the class of partially solvable models.…”

Section: Introductionmentioning

confidence: 99%

Approximate Solution of Schrödinger Equation with Pseudo-Gaussian Potential Viewed as a Perturbation

Lute

Annals of West University of Timisoara - Physics

2015

Self Cite

We consider the Schrödinger equation with pseudo-Gaussian potential and point out that it is basically made up by a term representing the harmonic oscillator potential and an additional term, which is actually a power series that converges rapidly. Based on this observation the system can be considered as a perturbation of harmonic oscillator. The perturbation method is used to approximate the energy levels of pseudo- Gaussian oscillator. The results are compared with those obtained in the analytic and numeric case.

Int J of Quantum Chemistry

Few electron systems confined in Gaussian potential wells and connection to Hooke atoms

Telleria‐Allika

Mercero

Ugalde

et al. 2022

In this work, we have computed and implemented one-body integrals concerning Gaussian confinement potentials over Gaussian basis functions. Then, we have set an equivalence between Gaussian and Hooke atoms and we have observed that, according to singlet and triplet state energies, both systems are equivalent for large confinement depth for a series of even number of electrons n = 2, 4, 6, 8 and 10.