This is the first in a series of articles in which we study the rotating Morse potential model for diatomic molecules in the tridiagonal J-matrix representation. Here, we compute the bound states energy spectrum by diagonalizing the finite dimensional Hamiltonian matrix of H 2 , LiH, HCl and CO molecules for arbitrary angular momentum. The calculation was performed using the J-matrix basis that supports a tridiagonal matrix representation for the reference Hamiltonian. Our results for these diatomic molecules have been compared with available numerical data satisfactorily. The proposed method is handy, very efficient, and it enhances accuracy by combining analytic power with a convergent and stable numerical technique.

The bound state energies for the exponential-cosine-screened Coulomb potential were calculated by using the Gauss quadrature method. The resonance energies were calculated using the complex rotation method and were then used as a seed for our J-matrix approach in order to achieve improved results. The calculated bound and resonance state energies are compared with the available numerical data in this paper. The trajectories of the resonance states in the complex E-plane are also shown. New data, for both bound and resonance state energies close to the crossover region of the transition from bound to resonance, have been reported for guiding future studies.

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We use the tools of the J-matrix method to evaluate the S-matrix and then deduce the bound and resonance states energies for singular screened Coulomb potentials, both analytic and piecewise differentiable. The Jmatrix approach allows us to absorb the 1/r singularity of the potential in the reference Hamiltonian, which is then handled analytically. The calculation is performed using an infinite square integrable basis that supports a tridiagonal matrix representation for the reference Hamiltonian. The remaining part of the potential, which is bound and regular everywhere, is treated by an efficient numerical scheme in a suitable basis using Gauss quadrature approximation. To exhibit the power of our approach we have considered the most delicate region close to the boundunbound transition and compared our results favorably with available numerical data.

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