Calculation of the first excited (1)S(e) state of the He atom using supersymmetric quantum mechanics and extension to the nth excitation
Usually the renormalized Numerov (RN) algorithm is used to solve the set of coupled differential equations of the few-body system, mainly for the ground state. The straightforward approach of this algorithm faces some serious problems of convergence to calculate the excited states. Here we present an alternative method using the supersymmetric quantum mechanics formalism to a multidimensional bound-state problem. The problem of convergence is avoided in this approach by searching for the ground state of the partner potential. Application of this formalism to the first excited (1)S(e) state of the He atom gives excellent results; it is much better than the conventional RN algorithm and the hyperspherical adiabatic approximation. We also indicate how the method can be generalized to the nth excited state.
Das
TK
Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Calcutta 700009, India.
Chakrabarti
B