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Approximate Solution of GCF PDM Schrödinger Equation for a Symmetrical Modified Pöschl–Teller Potential by GCF Laplace Transform Method

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Abstract

In this paper, we introduce a new definition of the general conformable fractional (GCF) Laplace transform with respect to the function Φ generated by the fractional conformable function ϕ. By the new definition, the usual Laplace transform and the \(\rho -\) Laplace transform are special cases of the GCF Laplace transform. We prove several important properties of these GCF Laplace transforms. In addition, we also define the GCF cylindrical coordinates system and derive the GCF Laplace operator on these coordinates. Furthermore, we study the approximate solution of the GCF position-dependent mass (PDM) Schrödinger equation for a symmetrical modified Pöschl-Teller potential in the GCF cylindrical coordinate system by using the GCF Laplace transform method. The GCF radial wave function and GCF energy eigenvalue are obtained from the approximate solution of the GCF Schrödinger equation. The behavior of the bound state conformable fractional energy levels was demonstrated and analyzed by using the computational method for various values of the order of conformable fractionality \(\alpha\), quantum number, and mass of the molecule. Moreover, the maximum conformable fractional energy-eigenvalue is obtained with respect to the influence of the order of conformable fractionality \(\alpha\) and mass for diatomic molecules \({\mathrm{H}}_{2}\), LiH, and HCl.

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Data Availability

We do not use primary or secondary data in our paper. We give the values of parameters from literature [35].

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Acknowledgements

The authors would like to express their gratitude to Sebelas Maret University for supporting and funding this research during the 2022 academic year.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Surakarta, 57126, Indonesia

    Supriyadi Wibowo

  2. Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Surakarta, 57126, Indonesia

    A. Suparmi & C. Cari

  3. Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, 55281, Indonesia

    Christiana Rini Indrati

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  1. Supriyadi Wibowo
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Supriyadi Wibowo, A Soeparmi, Christiana Rini Indrati, and C Cari wrote the main manuscript text and all authors reviewed the manuscript

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Correspondence to Supriyadi Wibowo.

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Wibowo, S., Suparmi, A., Indrati, C.R. et al. Approximate Solution of GCF PDM Schrödinger Equation for a Symmetrical Modified Pöschl–Teller Potential by GCF Laplace Transform Method. Int J Theor Phys 62, 222 (2023). https://doi.org/10.1007/s10773-023-05464-z

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