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This is the first in a series of articles in which we study the rotatingMorse potential model for diatomic molecules in the tridiagonal J-matrixrepresentation. Here, we compute the bound states energy spectrum bydiagonalizing the finite dimensional Hamiltonian matrix of H2, LiH, HCl and COmolecules for arbitrary angular momentum. The calculation was performed usingthe J-matrix basis that supports a tridiagonal matrix representation for thereference Hamiltonian. Our results for these diatomic molecules have beencompared with available numerical data satisfactorily. The proposed method ishandy, very efficient, and it enhances accuracy by combining analytic powerwith a convergent and stable numerical technique.

The rotating Morse potential model for diatomic molecules in the tridiagonal J-matrix representation: I. Bound states