Symmetry, Volume 16, Issue 3
2024 March - 126 articles
Cover Story: Single-shot factorization uses a general ansatz for the factorization of a single-particle Hamiltonian; here, we use a form based on confluent hypergeometric functions. By adjusting the parameters in the factorization to ensure normalizable wavefunctions, all energy eigenvalues and wavefunctions are determined at once. The approach is equivalent to Natanzon’s approach, which instead works directly with the confluent hypergeometric differential equation. This approach is halfway between the conventional Schrödinger equation approach and the Schrödinger factorization chain. Here, we depict the two bound states of a Natanzon potential that can be solved exactly with this approach. The dashed lines indicate the energies of each state, and the black line is the potential (which asymptotes to zero for large positive x). View this paper - Issues are regarded as officially published after their release is announced to the table of contents alert mailing list .
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