Abstract
Some computational techniques are presented here. A method is presented for solution of a single differential eigenvalue equation, subject to boundary conditions at the origin and at infinity. Next solution of a system of coupled differential eigenvalue equations (CDEE) is discussed. First an exact numerical algorithm, viz., renormalized Numerov (RN) method is presented. Next approximation methods are discussed. Introduction of a hypercentral average enhances the rate of convergence. Hyperspherical adiabatic approximation (HAA) reduces the CDEE to a single differential equation. Applicability, accuracy, and numerical procedure of HAA are discussed. Finally, a method is presented for handling tricky integrals (involving extremely fast changing integrand) in potential matrix element.
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Das, T.K. (2016). Computational Techniques. In: Hyperspherical Harmonics Expansion Techniques. Theoretical and Mathematical Physics. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2361-0_10
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DOI: https://doi.org/10.1007/978-81-322-2361-0_10
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