Correlated One Particle States

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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
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One Particle Theory

• N-particle State totally determined by
• A set of Generalized Spin Orbitals (GSOs)
  spanning one particle space
• A set of occupation numbers of these GSOs

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Generalized Spin Orbitals
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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
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This Gives

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First Order Reduced Density Operator FORDO
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Many to One
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Note
Produce the same FORDO
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An Example of a Correlated N Particle State
Determined by One Particle Properties
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Antisymmetrized Geminal Power State (AGP)
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Geminal
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A. J. Coleman has proved (Reduced Density
Matrices pp 142-144), that
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Thus

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If the geminal is more than two fold degenerate
then the invariance group is bigger
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But are in general different as they have
different

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Second Order Reduced Density Operators (SORDOs)