Theoretical study of electronic and optical properties in doped quantum structures with Razavy confining potential: effects of external fields

Dakhlaoui, Hassen; Gil-Corrales, John A.; Morales, A. L.; Kasapoğlu, E.; Radu, A.; Restrepo, R.L.; Tulupenko, V.; Vinasco, J.A.; Duque, C.A.

doi:10.1007/s10825-022-01859-z

Cited by 5 publications

(1 citation statement)

References 89 publications

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“…Among the well-known DWP models are the symmetric-hyperbolic DWP including the Razavy bistable potential (RBP) which successfully described molecular torsion oscillations with 𝑛 and 2𝑛-fold resistance [11], the Konwent potential which successfully modeled nucleons in the nucleus [12], and the double sinh Gordon (DSHG) potential which was applied to sink and anti-sink calculations in thermodynamics [13]. Nowadays, hyperbolic DWPs are used to investigate the electrical and optical properties in semi conductor by investigating the role of structure parameters [14][15][16], applied external fields [17][18][19][20] and applied magnetic fields [21]. Despite having many possible applications, the solutions of symmetric-hyperbolic DWP are not complete, where quasi-exact solvable (QES) of the eigen-energies and eigenfunctions have been obtained for some limited lowest states only [11][12][13]22].…”

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confidence: 99%

Estimation of Energy Separation in Tunelling States in Symmetric-Hyperbolicus Double-Well Potential Problem using Filter Method

Abdurrouf,

Saroja,

Nurhuda

2024

Trends Sci

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Double well potential (DWP) plays an important role in quantum physics but its analytical exact solutions are incomplete, except for some limited quasi-exact solvable (QES) and therefore numerical solutions are still required. This paper is aimed to obtain numerical solution of the recently proposed symnetric-hyperbolicus DWP and by using our newly developed filter method. The filter method is able to produce eigen-energies and eigenfunctions those are in accordance with the exact analytical results. Next, we obtain the dependence of the ground state energy and the energy separation between the 2 lowest states on the DWP parameter k. For large k, the 2 lowest energy levels are below the potential barrier so the eigenfunctions penetrate the barrier, so the 2 lowest energy levels can be considered as the result of a single energy split. In this case, we observe that the energy separation is an exponential function k, as opposed to a linear function for smaller k in the non tunelling region. The exponential trend of the numerical results is in good agreement with the theoretical approach and allows one to estimate the 2 lowest energies for a given k. HIGHLIGHTS For small , the two lowest energy levels lie above the barrier potential, where both ground state and the energy separation is a linier function of For large , the two lowest energy levels lie below the barrier potential so that the eigenfunction penetrates the barrier. As a result, the two lowest energy levels can be thought of as splitting energy states. In this case, we observe that the energy separation is an exponential function . Since also depends on , it is possible to estimate the two lowest energy levels The exponential trend of the numerical results for large agrees well with the theoretical approach, shown by the linear relationship between and the classical actions in the classical forbidden regions, GRAPHICAL ABSTRACT

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