TY - JOUR
T1 - A scheme of numerical solution for three-dimensional isoelectronic series of hydrogen atom using one-dimensional basis functions
AU - Rahman, Faiz Ur
AU - Zhao, Rundong
AU - Sarwono, Yanoar Pribadi
AU - Zhang, Rui-Qin
PY - 2018/10/5
Y1 - 2018/10/5
N2 - The solution of three-dimensional Schrödinger wave equations of the hydrogen atoms and their isoelectronic ions (Z = 1 − 4) are obtained from the linear combination of one-dimensional hydrogen wave functions. The use of one-dimensional basis functions facilitates easy numerical integrations. An iteration technique is used to obtain accurate wave functions and energy levels. The obtained ground state energy level for the hydrogen atom converges stably to −0.498 a.u. The result shows that the novel approach is efficient for the three-dimensional solution of the wave equation, extendable to the numerical solution of general many-body problems, as has been demonstrated in this work with hydrogen anion.
AB - The solution of three-dimensional Schrödinger wave equations of the hydrogen atoms and their isoelectronic ions (Z = 1 − 4) are obtained from the linear combination of one-dimensional hydrogen wave functions. The use of one-dimensional basis functions facilitates easy numerical integrations. An iteration technique is used to obtain accurate wave functions and energy levels. The obtained ground state energy level for the hydrogen atom converges stably to −0.498 a.u. The result shows that the novel approach is efficient for the three-dimensional solution of the wave equation, extendable to the numerical solution of general many-body problems, as has been demonstrated in this work with hydrogen anion.
KW - ground state
KW - hydrogen atom
KW - iteration
KW - one-dimensional basis function
KW - Schrödinger wave equations
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U2 - 10.1002/qua.25694
DO - 10.1002/qua.25694
M3 - 21_Publication in refereed journal
VL - 118
JO - International Journal of Quantum Chemistry
JF - International Journal of Quantum Chemistry
SN - 0020-7608
IS - 19
M1 - e25694
ER -