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4. ENERGY LEVELS AND ROOT-MEAN-SQUARE SPEEDS OF A SYSTEM IN PÖSCHL-TELLER TYPE POTENTIAL by Bitrus B.M, Nwabueze C.M, Najoji S.D Volume 59 (January – March 2021 Issue)
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ENERGY LEVELS AND ROOT-MEAN-SQUARE SPEEDS OF A SYSTEM IN PÖSCHL-TELLER TYPE POTENTIAL

Bitrus B.M1., Nwabueze C.M2., Najoji S.D3.

Department of Physics, Faculty of Science, Taraba State University, P.M.B. 1176, Jalingo Taraba State, Nigeria

Department of Basic Sciences, School of General and Remedial Studies, The Federal Polytechnic, P.M.B. 1006, Damaturu, Yobe State, Nigeria

Abstract

In this work, the improved quantization rule was applied to derive closed form expression for bound state energy eigenvalues of the Pöschl-Teller type potential, normalized expression for radial eigenfunctions were obtained by ansatz solution technique. The improved Greene-Aldrich approximation scheme was used to model the centrifugal term of the Schrödinger equation, the expression for bound state energy eigenvalues and radial wave functions agrees totally with literature data for the Pöschl-Teller type potential when reduced to s-wave. With the help of the formula for energy eigenvalues. Expression for root-mean-square speed was deduced within the confines of Hellmann-Feynman theorem, it was further observed that the root-mean-square speed of the system increases monotonically with the potential strength of the potential and is smaller for small values of screening parameters.

Keywords: Effective potential, root-mean-square speed, proper quantization rule, Pöschl-Teller type potential, Schrödinger equation 

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