ENERGY SPECTRUM AND SOME USEFUL EXPECTATION VALUES OF THE TIETZ-HULTHÉN POTENTIAL

Authors

  • Bako M. Bitrus
  • U Wadata
  • C. M. Nwabueze
  • E. S. Eyube

DOI:

https://doi.org/10.33003/fjs-2021-0501-614

Keywords:

Energy spectrum, SUSYQM, Tietz-Hulthén potential, Hellmann-Feynman theorem, expectation values

Abstract

In this paper, concept of supersymmetric quantum mechanics has been employed to derive expression for bound state energy eigenvalues of the Tietz-Hulthén potential, the corresponding equation for normalized radial eigenfunctions were deduced by ansatz solution technique. In dealing with the centrifugal term of the effective potential of the Schrödinger equation, a Pekeris-like approximation recipe is considered. By means of the expression for bound state energy eigenvalues and radial eigenfunctions, equations for expectation values of inverse separation-squared and kinetic energy of the Tietz-Hulthén potential were obtained from the Hellmann-Feynman theorem. Numerical values of bound state energy eigenvalues and expectation values of inverse separation-squared and kinetic energy the Tietz-Hulthén potential were computed at arbitrary principal and angular momentum quantum numbers. Results obtained for computed energy eigenvalues of Tietz-Hulthén potential corresponding to Z = 0 and V0 = 0 are in excellent agreement with available literature data for Tietz and Hulthén potentials respectively. Studies have also revealed that increase in parameter Z results in monotonic increase in the mean kinetic energy of the system. The results obtained in this work may find suitable applications in areas of physics such as: atomic physics, chemical physics, nuclear physics and solid state physics

References

Akoroda, M.O. (1990). Ethnobotany of Telfairia occidentalis among Igbos of Nigeria. Economic Botany, 44(1):29-39.

Bell, M. (2004). Plant parasitic nematodes: Lucid key to 30 genera of plant-parasitic nematodes: retrieved online on 13th September, 2011 from http://www.lucicentral.com/keys/nematodes.

Doncaster, C. C. (1962). A counting dish for nematodes. Nematologica, 7:33-36.

Dropkin, V.H., Smith, W. L. and Myers, R. F. (1960). Recovery of nematodes from infected roots by maceration. Nematologica, 5: 285-288.

Edet, J., Udoh, S. and Akpan, B. (2007). Measuring technical efficiency of waterleaf (Talinum triangulare). American-Eurasian Journal of Agriculture & Environmental Science, 2 (5): 518-522

Ekpe, E.O. and Obiefuna, J.C. (1977). Effects of plant population and harvesting frequency on the agronomic characteristics and yield of waterleaf, Talinum triangulare in the Southeastern Nigeria

Etim, D. O., Eleng, I. E., Bassey, R. A. and Igwe, C. B. (2020). Prevalence of root-knot

nematodes (Meloidogyne species) on Waterleaf (Talinum triangulare) in three locations in University of Calabar. South Asian Journal of Parasitology, 4(3): 18-26

Eyo, E.O., Ekpe, E.O. and Ogban, P.I. (2000). Waterleaf (Talinum triangulare Wild) production in south eastern Nigeria: Existing practices, suggestions for increased productivity and profit. Global Journal of Pure and Applied Sciences, 7: 421-426.

Hammer, O, Harper, D.A.T. and Ryan, P. D. (2001). PAST: Paleontological statistic software package for education and data analysis. Paleontological Electronica 4(1): 9 pp

Ekpo. I.A., Osuagwu, A.N., Okpako, E.C., Agbor, R.B., Kalu, S.E. and Okigbo, A.U. (2013). Tolerance of Talinum triangulare (Waterleaf) to crude oil polluted soil. American International Journal of Biology, 1(1):13-20.

Grubben, G. J. H. (2004). Vegetables: Talinum triangulare (Waterleaf). Plant Resources of Tropical Africa (Volume 2). ISBN 9057821478;9789057821479, 667 pp

Kent, M. and Coker, P. (1996). Vegetation description and analysis. A practical approach. John Wiley and Sons, NY, 363 pp

Khan, M.R. and Khan, M.W. (1994). Single and interactive effects of root-knot nematode and coal-smoke on okra. New Phytologist, 126: 337-342.

Nicol, J.M. (2002). Important nematode pests. In: Curtis, B.C., Rajaram, S., Gomez, M. (eds), Breadwheat improvement and production. FAO Plant Production and Protection Series, pp: 567.

Osei, K., Addico, R., Nafeo, A., Edu-Kwarteng, A., Agyemang, A., Danso, Y., Sackey-Asante, J. (2011). Effect of some organic waste extracts on hatching of Meloidogyne incognita eggs. African Journal of Agricultural Research, 6 (10):2255-2259.

SAS. (2007). Statistical Analysis System User’s Guide. SAS Institute Inc. Carry N.C. USA.

Savary, S. and Willocquet, L. (2014). Simulation modeling in botanical epidemiology and crop loss analysis. The American Phytopathological Society. APSnet The Plant Health Instructor, 173 p.

Schippers, R.R. (2000). African indigenous vegetables. An overview of the cultivated species. Chatham, United Kingdom: Natural resources Institute? ACP-EU Technical Centre for Agriculture and Rural Co-operation, 214 pp.

Sikora, A. and Fernández, E. (2005). Nematode parasites of vegetables. In: Luc, M.;

Sikora R. A.; Bridge J. (eds). Plant Parasitic Nematodes in Subtropical and Tropical Agriculture. Wallingford, UK: CAB International, pp 319-392

Sobrasuaipiri, S. (2016). Vulnerability and adaptive capacity in livelihood responses to oil spill in Bodo, Niger Delta. A thesis submitted in partial fulfilment of the requirements of the University of Brighton for the degree of Doctor of Philosophy, 259 pp

Thompson, H.C., Kelly, W.C. and Yonnis, S.E. (1975). Vegetable crops. McGraw-Hill Book Company, Inc. New York. pp 37- 40.

Van Epenhuijsen, C.W. (1974). Growing native vegetables in Nigeria. Food and Agriculture Organization of the United Nations, Rome, 113 pp.

Whitehead, A. G. and Hemming, J.R. (1965). A comparison of some quantitative methods of extracting small vermiform nematodes from soil. Annals of Applied Biology, 55:25-38

Published

2021-07-06

How to Cite

Bitrus, B. M., Wadata, U., Nwabueze, C. M., & Eyube, E. S. (2021). ENERGY SPECTRUM AND SOME USEFUL EXPECTATION VALUES OF THE TIETZ-HULTHÉN POTENTIAL. FUDMA JOURNAL OF SCIENCES, 5(2), 255 - 263. https://doi.org/10.33003/fjs-2021-0501-614