Exact solutions for semirelativistic problems with non-local potentials

Details Exact solutions for semirelativistic problems with non-local potentials Exact solutions for semirelativistic problems with non-local potentials

2005-12-22

arxiv.org/abs/math-ph/0512079v1

J. Phys. A 39, 903 - 912 (2006)

Physics

Mathematical Physics

13 pages, 3 figures

Scientific paper

10.1088/0305-4470/39/4/011

It is shown that exact solutions may be found for the energy eigenvalue problem generated by the class of semirelativistic Hamiltonians of the form H = sqrt{m^2+p^2} + hat{V}, where hat{V} is a non-local potential with a separable kernel of the form V(r,r') = - sum_{i=1}^n v_i f_i(r)g_i(r'). Explicit examples in one and three dimensions are discussed, including the Yamaguchi and Gauss potentials. The results are used to obtain lower bounds for the energy of the corresponding N-boson problem, with upper bounds provided by the use of a Gaussian trial function.

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