Q-Deformed Harmonic Oscillator and Morse-like Anharmonic Potential

Vinh, Ngo Gia; Ngu, Man Van; Lan, Nguyen Tri; Thanh, Luu Thi Kim; Việt, Nguyễn Ái

doi:10.1088/1742-6596/627/1/012022

Cited by 6 publications

(4 citation statements)

References 9 publications

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“…TABLE I: Energy level and q-deformation dependence of Shanon information entropy, disequilibrium and complexity for q-deformed harmonic oscillator. After quantifying the complexity of q-oscillator, here we consider, as an second example, q-deformed Morse potential [17][18][19][20]. The general form of the q-deformed Morse potential is expressed in the Ref.…”

Section: Complexity Study Of Q-deformed Potentialsmentioning

confidence: 99%

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Complexity Study of a Single Particle Under q-Deformed Potentials

Nutku¹,

Sen²,

Aydıner³

2018

Preprint

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We have studied the variation of the position space statistical complexity measure defined by López-Ruiz, Mancini, and Calbet such as the product of exponential of the Shannon information entropy and the disequilibrium by using the 1D-normalized probability densities derived from solutions of the Schrödinger equation corresponding to the q-deformed harmonic oscillator and qdeformed Morse potentials. An analysis of the numerical results in terms of Shannon information entropy, disequilibrium and complexity measure are presented. In q-deformed harmonic oscillator, q-dependence of the complexity shows a minimum point for all excited energy levels. In the case of q-deformed Morse Potential, complexity decreases with increasing q for the investigated diatomic molecules.

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Section: Complexity Study Of Q-deformed Potentialsmentioning

confidence: 99%

“…Some recent works are the investigation and comparison of the energy spectrum of q-oscillator and Morse-like anharmonic potential in Ref. [20] and derivation of the exact normalized wave functions for the q-deformed screened Coulomb Hulthen potential in Ref. [21] etc.…”

Section: Introductionmentioning

confidence: 99%

Complexity Study of a Single Particle Under q-Deformed Potentials

Nutku¹,

Sen²,

Aydıner³

2018

Preprint

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“…There are a few related works on the

q

‐deformations of the systems. Among these,

q

‐harmonic oscillator is the most extensively studied one in the

q

‐deformed quantum mechanics with the

q

‐Hamiltonians [1, 3, 6–8]. There are many applications in several fields of physics and chemistry [4, 8].…”

Section: Introductionmentioning

confidence: 99%

“…Among these,

q

‐harmonic oscillator is the most extensively studied one in the

q

‐deformed quantum mechanics with the

q

‐Hamiltonians [1, 3, 6–8]. There are many applications in several fields of physics and chemistry [4, 8].…”

Section: Introductionmentioning

confidence: 99%

Spectrum of a q‐deformed Schrödinger equation by means of the variational method

Doğan Çalışır,

Turan,

Sevinik Adıgüzel

2023

Math Methods in App Sciences

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In this work, the ‐deformed Schrödinger equations defined in different form of the ‐Hamiltonian for ‐harmonic oscillator are considered with symmetric, asymmetric, and non‐polynomial potentials. The spectrum of the ‐Hamiltonian is obtained by using the Rayleigh‐Ritz variational method in which the discrete ‐Hermite I polynomials are taken as the basis. As applications, ‐harmonic, purely ‐quartic, and ‐quartic oscillators are examined in the class of symmetric polynomial potentials. Moreover, the ‐version of Gaussian potential for an example of a non‐polynomial symmetric potential and a specific example of ‐version of asymmetric double well potential are presented. Numerous results are given for these potentials for several values of . The limit relation as is discussed. The obtained results of ground‐ and excited‐state energies of the purely ‐quartic oscillator and the accuracy of the ground‐state energy levels are compared with the existing results. Also, the results are compared with the classical case appearing in the literature in the limiting case .

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