# 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 fall-off 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 two-body 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):
- LLNL-JRNL-680078

Journal ID: ISSN 0177-7963

- Grant/Contract Number:
- AC52-07NA27344

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Few-Body Systems

- Additional Journal Information:
- Journal Name: Few-Body Systems; Journal ID: ISSN 0177-7963

- 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/s00601-016-1126-9.

```
Papadimitriou, G.
```*Calculation of Expectation Values of Operators in the Complex Scaling Method*. United States. doi:10.1007/s00601-016-1126-9.

```
Papadimitriou, G. Tue .
"Calculation of Expectation Values of Operators in the Complex Scaling Method". United States.
doi:10.1007/s00601-016-1126-9. 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 fall-off 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 two-body Gaussian model and also applications using realistic interactions.},

doi = {10.1007/s00601-016-1126-9},

journal = {Few-Body Systems},

number = ,

volume = ,

place = {United States},

year = {Tue Jun 14 00:00:00 EDT 2016},

month = {Tue Jun 14 00:00:00 EDT 2016}

}