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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

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Expectation values in two-component relativistic theories.

Junji Seino¹, Wataru Uesugi, Masahiko Hada

¹Department of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji-shi, Tokyo 192-0397, Japan.

The Journal of Chemical Physics

|May 6, 2010

Summary

This study numerically confirms that infinite-order Douglas-Kroll (IODK) wave functions and picture-changed operators yield equivalent expectation values to four-component methods for atomic calculations.

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Area of Science:

Quantum Chemistry
Relativistic Quantum Mechanics

Background:

Four-component relativistic wave functions are accurate but computationally expensive.
Two-component methods, like the infinite-order Douglas-Kroll (IODK) transformation, offer a computationally efficient alternative.
Assessing the equivalence of expectation values between these methods is crucial for practical applications.

Purpose of the Study:

To numerically investigate the equivalence of expectation values calculated by four-component wave functions and two-component IODK wave functions.
To analyze the accuracy of specific expectation values, and , using picture-changed operators.

Main Methods:

Numerical evaluation of expectation values using four-component and two-component (IODK) wave functions.
Application of picture-changed 2x2 operators at various approximation levels.
Inclusion and discussion of the two-electron Coulomb term's effect.

Main Results:

The accuracy of expectation values primarily depends on the wave function's approximation level.
expectation values are sensitive to both wave function accuracy and the precision of picture-changed operators.
Numerical results demonstrate essential equivalence between IODK and four-component methods for the studied expectation values.

Conclusions:

The infinite-order Douglas-Kroll transformation provides a reliable and accurate two-component approach for calculating expectation values.
Picture-changed operators are vital for maintaining accuracy in two-component relativistic calculations.
IODK wave functions and associated operators are suitable alternatives to computationally intensive four-component methods.