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Abstract
A new numerical approach (finite-element method) to solving one-dimensional Schrödinger problems is discussed. Its effectiveness is demonstrated in solving the nontrivial finite well and Morse potential problems. Moreover, it is shown by a case study of 16 low-lying vibrational states of Li2 that the finite-element method can achieve the same order of accuracy more easily than the better known Numerov–Cooley method.
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