Kisoglu Hasan Fatih, Yanar Hilmi, Aydogdu Oktay, Salti Mustafa
Department of Basic Sciences, Faculty of Maritime, Mersin University, 33200, Mersin, Turkey.
Department of Physics, Faculty of Science and Letters, Mersin University, 33343, Mersin, Turkey.
J Mol Model. 2019 May 2;25(5):143. doi: 10.1007/s00894-019-4021-8.
We tackle with the Dirac equation in the presence of the general molecular potential (GMP). The spin symmetric solution of the relativistic wave equation is obtained by considering the Pekeris-type approximation scheme to deal with the centrifugal term, and in order to solve second-order differential equation, the asymptotic iteration method (AIM) is used. The closed form of the energy eigenvalue equation is found out for any values of the angular momentum quantum number. We calculate the relativistic vibrational bound state energies of 5Δ state of Na molecule and compare them with the Rydberg-Klein-Rees (RKR) data. We show that relativistic vibrational energies of this molecule, which are found in the spin symmetric case, are more convenient with experimental RKR data than non-relativistic vibrational energies. We also obtain normalization constant by considering inductive approach and investigate the radial eigenfunctions and probability density functions corresponding to different eigenvalues graphically for the Na(5Δ) molecule.
我们研究存在一般分子势（GMP）时的狄拉克方程。通过考虑处理离心项的佩克里斯型近似方案，得到相对论波动方程的自旋对称解，并且为了求解二阶微分方程，使用了渐近迭代法（AIM）。针对角动量量子数的任意值，求出了能量本征值方程的封闭形式。我们计算了钠分子5Δ态的相对论振动束缚态能量，并将其与里德堡 - 克莱因 - 里斯（RKR）数据进行比较。我们表明，在自旋对称情况下发现的该分子的相对论振动能量比非相对论振动能量更符合实验RKR数据。我们还通过考虑归纳法获得归一化常数，并以图形方式研究了钠（5Δ）分子对应于不同本征值的径向本征函数和概率密度函数。
