Abstract
A molecular potential model is proposed and the solutions of the radial Schrӧdinger equation in the presence of the proposed potential is obtained. The energy equation and its corresponding radial wave function are calculated using the powerful parametric Nikiforov–Uvarov method. The energies of cesium dimer for different quantum states were numerically obtained for both negative and positive values of the deformed and adjustable parameters. The results for sodium dimer and lithium dimer were calculated numerically using their respective spectroscopic parameters. The calculated values for the three molecules are in excellent agreement with the observed values. Finally, we calculated different expectation values and examined the effects of the deformed and adjustable parameters on the expectation values.
Highlights
A molecular potential model is proposed and the solutions of the radial Schrӧdinger equation in the presence of the proposed potential is obtained
The present study wants to examine an approximate solutions of the Schrӧdinger equation with a new modified and deformed exponential-type molecular potential model confined on a cesium dimer, sodium dimer and lithium dimer
The results obtained with q0 = q1 = −1 are higher than their counterpart obtained with q0 = q1 = 1
Summary
Setting the wave function ψ(r) = Un,l(r)Ym,l(θ , φ)r−1, and consider the radial part of the Schrӧdinger equation, Eq (7) becomes d2Unl(r) dr[2]. Where V (r) is the interacting potential given in Eq (1), Enl is the non-relativistic energy of the system, is the reduced Planck’s constant, μ is the reduced mass, n is the quantum number,Unl(r) is the wave function. Schrӧdinger equation with the deformed exponentialtype potential turns to be d2Unl(y) dy[2]. Comparing Eq (9) with Eq (3), the parametric constants in Eq (6) are obtain as follows. Substituting the parameters in Eq (13) into Eq (4), we have the energy equation for the system as. The corresponding wave function is obtain when the values of α10 to α13 in Eq (6) are substituted into Eq (5), Un(y)
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