Numerical Calculation of Energy Eigen-values of the Hydrogen Negative Ion in the 2p^2 Configuration by Using the Variational Method

Yosef Robertus Utomo; Guntur Maruto; Agung Bambang Setio Utomo; Pekik Nurwantoro; Sholihun Sholihun

doi:10.22146/jfi.v24i1.53331

Numerical Calculation of Energy Eigen-values of the Hydrogen Negative Ion in the 2p^2 Configuration by Using the Variational Method

https://doi.org/10.22146/jfi.v24i1.53331

Yosef Robertus Utomo^(1*), Guntur Maruto⁽²⁾, Agung Bambang Setio Utomo⁽³⁾, Pekik Nurwantoro⁽⁴⁾, Sholihun Sholihun⁽⁵⁾

(1) Universitas Gadjah Mada
(2) Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas GadjahMada, Sekip Utara BLS 21 Yogyakarta 55281
(3) Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas GadjahMada, Sekip Utara BLS 21 Yogyakarta 55281
(4) Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas GadjahMada, Sekip Utara BLS 21 Yogyakarta 55281
(5) Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas GadjahMada, Sekip Utara BLS 21 Yogyakarta 55281
(*) Corresponding Author

Abstract

Calculation of energy eigen value of hydrogen negative ion (H − ) in 2p^2 configuration using the method of variation functions has been done. A work on H − can lead to calculations of electric multipole moments of a hydrogen molecule. The trial function is a linear combination of 8 expansion terms each of which is related to the Chandrasekhar’s basis. This work produces a series of 7 energy eigen values which converges to a value of −0.2468 whereas the value of this convergence is expected to be −0.2523. This deviation from the expected value is mainly due to the elimination of interelectronic distance (u) coordinate. The values of the exponent parameters used in this work contribute also to this deviation. This variational method will be applied to the construction of some energy eigen functions of Hv2 .

Keywords

Variational method, energy eigen values, hydrogen negative ion.

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