谁来讲（高量）：Perturbative and nonperturbative studies with the delta function potential

Nabakumar Bera, Kamal Bhattacharyya, and Jayanta K. Bhattacharjeea, Am. J. Phys. 76 (3), 250, March 2008

We show that the δ-function potential can be exploited along with perturbation theory to yield the
result of certain infinite series. The idea is that any exactly soluble potential, if coupled with a

function potential, remains exactly soluble. We use the strength of the
function as an expansion
parameter and express the second-order energy shift as an infinite sum in perturbation theory. The
analytical solution is used to determine the second-order energy shift and hence the sum of an
infinite series. By an appropriate choice of the unperturbed system, we can show the importance of
the continuum in the energy shift of bound states.

相关链接：http://arxiv.org/PS_cache/arxiv/pdf/0809/0809.4607v1.pdf