首页|A power series analysis of bound and resonance states of one-dimensional Schrodinger operators with finite point interactions
A power series analysis of bound and resonance states of one-dimensional Schrodinger operators with finite point interactions
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NSTL
Elsevier
In this paper we consider one-dimensional Schrodinger operators S(q)u(x) = -(-d(2)/dx(2) + q(r) (x) + q(s) (x)) u(x), x is an element of R, where q(r) is an element of L-infinity (R) is a regular potential with compact support, and q(s) is an element of D' (R) is a singular potential q(s) (x) = Sigma(N)(j=1)(alpha(j)delta(x - x(j)) + beta(j)delta'(x - x(j))), alpha(j), beta(j) is an element of C that involves a finite number of point interactions. The eigenenergies associated to the bound states and the complex energies associated to the resonance states of operator S-q are given by the zeros of certain characteristic functions eta(+/-) that share the same structure up to an algebraic sign. The functions eta(+/-) are obtained explicitly in the form of power series of the spectral parameter, and the computation of the coefficients of the series is given by a recursive integration procedure. The results here presented are general enough to consider arbitrary regular potentials q(r) is an element of L-infinity (R) with compact support, even complexvalued, and point interactions with complex strengths alpha(j), beta(j) (j = 1,..., N). Moreover, our approach leads to an efficient numerical treatment of both the bound and resonance states. (C) 2021 Elsevier Inc. All rights reserved.
Point interactionsOne-dimensional Schrodinger operatorsBound statesResonance statesSpectral parameter power seriesSPECTRAPOTENTIALSEQUATION
NSTL
Elsevier
