Calculation of the Eigenstates and Eigenvalues for the Power and Inverse-Power Hypercentral Potentials |
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Authors: | A A Rajabi |
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Institution: | (1) Physics Department, Shahrood University of Technology, P.O. Box 3619995161-316, Shahrood, Islamic Republic of Iran |
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Abstract: | The bound-state solutions to the hyperradial Schr?dinger equation is constructed for any general case comprising any hypercentral
power and inverse-power potentials. The hypercentral potential depends only on the hyperradius which itself is a function
of Jacobi relative coordinates that are functions of particle positions (r
1,r
2, … , and r
N
). This paper is mainly devoted to the demonstration of the fact that any ψ of the form ψ = power series × exp(polynomial)
= f(x) exp (g(x))] is potentially a solution of the Schr?dinger equation, where the polynomial g(x) is an ansatz depending on the interaction potential. |
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Keywords: | |
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