ISSN:
1089-7690
Source:
AIP Digital Archive
Topics:
Physics
,
Chemistry and Pharmacology
Notes:
The complex coordinate method (CCM) can be presented by carrying out a similarity transformation of the Hamiltonian Sˆ+1HˆSˆ−1 in order to correct the asymptotic behavior of the resonance eigenfunction, such that Sˆψres→0, whereas ψres→∞, as r→∞. Therefore, after the similarity transformation, the number of the particles is conserved in the coordinate space for any given time. Here, several different possibilities for Sˆ are presented, emphasizing the advantage of the representation of CCM by similarity transformation operators. A new extension of the complex coordinate method is that Sˆ∼exp[−θf 1/2(r)(∂/∂r) f 1/2(r)], where f(r) can be any function for which f(r)/r→1 as r→∞. Whereas, in the conventional CCM, f(r)=r. This new method enables one to select the "optimal'' path in the complex coordinate plane, which gets past the intrinsic nonanalyticities of the potential and provides the most stable resonance solution which can be obtained by a given number of basis functions.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.454275
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