Exact solutions for semirelativistic problems with non-local potentials
Richard L. Hall
Abstract
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 = sqrtm2+p2 + hatV, where hatV is a non-local potential with a separable kernel of the form V(r,r') = - sumi=1n vi fi(r)gi(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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