Calculation of Expectation Values of Operators in the Complex Scaling Method
Abstract
In the complex scaling method (CSM) provides with a way to obtain resonance parameters of particle unstable states by rotating the coordinates and momenta of the original Hamiltonian. It is convenient to use an L^{2} integrable basis to resolve the complex rotated or complex scaled Hamiltonian H_{θ} , with θ being the angle of rotation in the complex energy plane. Within the CSM, resonance and scattering solutions have falloff asymptotics. Furthermore, one of the consequences is that, expectation values of operators in a resonance or scattering complex scaled solution are calculated by complex rotating the operators. In this work we are exploring applications of the CSM on calculations of expectation values of quantum mechanical operators by using the regularized backrotation technique and calculating hence the expectation value using the unrotated operator. Moreover, the test cases involve a schematic twobody Gaussian model and also applications using realistic interactions.
 Authors:

 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1258519
 Report Number(s):
 LLNLJRNL680078
Journal ID: ISSN 01777963
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Accepted Manuscript
 Journal Name:
 FewBody Systems
 Additional Journal Information:
 Journal Name: FewBody Systems; Journal ID: ISSN 01777963
 Publisher:
 Springer
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Papadimitriou, G. Calculation of Expectation Values of Operators in the Complex Scaling Method. United States: N. p., 2016.
Web. doi:10.1007/s0060101611269.
Papadimitriou, G. Calculation of Expectation Values of Operators in the Complex Scaling Method. United States. doi:10.1007/s0060101611269.
Papadimitriou, G. Tue .
"Calculation of Expectation Values of Operators in the Complex Scaling Method". United States. doi:10.1007/s0060101611269. https://www.osti.gov/servlets/purl/1258519.
@article{osti_1258519,
title = {Calculation of Expectation Values of Operators in the Complex Scaling Method},
author = {Papadimitriou, G.},
abstractNote = {In the complex scaling method (CSM) provides with a way to obtain resonance parameters of particle unstable states by rotating the coordinates and momenta of the original Hamiltonian. It is convenient to use an L2 integrable basis to resolve the complex rotated or complex scaled Hamiltonian Hθ , with θ being the angle of rotation in the complex energy plane. Within the CSM, resonance and scattering solutions have falloff asymptotics. Furthermore, one of the consequences is that, expectation values of operators in a resonance or scattering complex scaled solution are calculated by complex rotating the operators. In this work we are exploring applications of the CSM on calculations of expectation values of quantum mechanical operators by using the regularized backrotation technique and calculating hence the expectation value using the unrotated operator. Moreover, the test cases involve a schematic twobody Gaussian model and also applications using realistic interactions.},
doi = {10.1007/s0060101611269},
journal = {FewBody Systems},
number = ,
volume = ,
place = {United States},
year = {2016},
month = {6}
}