Rényi and Tsallis Entropies of 2<i>p</i> Orbital Helium Atom

Abstract

In this paper, an analytical model of  2p orbital helium atom has been considered to quantify the values of the Rényi and Tsallis entropies along with their theoretical aspects. The normalized radial wave function used here (in atomic units) is obtained by solving the Schrödinger equation. The complete form of the coordinate space wave function is obtained by the use of the spherical harmonics. The momentum space wave function is obtained by taking the Fourier transform of the coordinate space wave function. The probability densities constituted with the respective coordinate and momentum space wave functions have been used to compute the numerical values of the Rényi and Tsallis entropies in the coordinate and momentum space for different values of the order β varying from 2 to 10. The computed values are presented in a tabular form. Further, it is mathematically demonstrated that in the limit of order β → 1, both the Rényi and Tsallis entropies lead to the Shannon entropy. Finally, an outlook of the present work has been summarized with some concluding remarks.