A novel angle-dependent potential and its exact solution

作者：Berkdemir Cueneyt^*

来源：Journal of Mathematical Chemistry, 2009, 46(1): 139-154.

DOI：10.1007/s10910-008-9447-7

• Diatomic molecule
• Novel angle-dependent (NAD) potential
• Coulomb potential and harmonic oscillator
• Nikiforov-Uvarov method
• Exact solution

The quantum mechanics of a diatomic molecule in a noncentral potential of the type V(r) = V(theta)(theta)/r(2) + V(r)(r) are investigated analytically. The theta-dependent part of the relevant potential is suggested for the first time as a novel angle-dependent (NAD) potential V(theta)(theta) = (h) over bar (2)/2 mu (gamma+beta sin(2) theta+alpha sin(4) theta/sin(2) theta cos(2) theta) and the radial part is selected as the Coulomb potential or the harmonic oscillator potential, i.e., V(r)(r) = -H/r or V(r)(r) = Kr(2), respectively. Exact solutions are obtained in the Schrodinger picture by means of a mathematical method named the Nikiforov-Uvarov (NU). The effect of the angle-dependent part on the solution of the radial part is discussed in several values of the NAD potential's parameters as well as different values of usual quantum numbers.

• 出版日期2009-6