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Correlated One Particle States

Correlated One Particle States B. Weiner Department of Physics, Pennsylvania State University DuBois PA 15801 J. V. Ortiz Department of Chemistry, Kansas State University, Manhattan, KS 66506-3701. One Particle Theory. N-particle State totally determined by

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Correlated One Particle States

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  1. Correlated One Particle States B. WeinerDepartment of Physics, Pennsylvania State UniversityDuBois PA 15801 J. V. Ortiz Department of Chemistry, Kansas State University, Manhattan, KS 66506-3701

  2. One Particle Theory • N-particle State totally determined by • A set of Generalized Spin Orbitals (GSO’s) spanning one particle space • A set of occupation numbers of these GSO’s

  3. Generalized Spin Orbitals

  4. Occupation Number is the probability that an electron belonging to a group of N-electrons in a specific N-electron state is somewhere in the region of space/spin described by

  5. This Gives

  6. First Order Reduced Density Operator FORDO

  7. & Many to One

  8. Note Produce the same FORDO

  9. An Example of a Correlated N Particle State Determined by One Particle Properties

  10. Antisymmetrized GeminalPower State(AGP)

  11. Geminal

  12. A. J. Coleman has proved (Reduced Density Matrices pp 142-144), that

  13. Thus

  14. If the geminal is more than two fold degenerate then the invariance group is bigger

  15. But are in general different as they have different

  16. Second Order Reduced Density Operators (SORDO’s)

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