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Local virial and tensor theorems.

Leon Cohen1

  • 1City University of New York, New York, New York 10065, United States. leon.cohen@hunter.cuny.edu

The Journal of Physical Chemistry. A
|August 26, 2011
PubMed
Summary
This summary is machine-generated.

Researchers demonstrate that the local virial theorem can be satisfied for any wave function and potential by selecting a specific local kinetic energy expression. This leads to infinite quasi-probability distributions for each kinetic energy choice.

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Area of Science:

  • Quantum mechanics
  • Theoretical physics

Background:

  • The virial theorem is a fundamental concept in quantum mechanics relating kinetic and potential energies.
  • Local formulations of the virial theorem are crucial for understanding electron density and atomic/molecular properties.

Purpose of the Study:

  • To demonstrate the general applicability of the local virial theorem.
  • To explore the relationship between local kinetic energy expressions and quasi-probability distributions.
  • To investigate the local tensor virial theorem.

Main Methods:

  • The study employs analytical methods to manipulate the local virial theorem equation.
  • It involves defining and analyzing different expressions for local kinetic energy.
  • The research explores the properties of quasi-probability distributions associated with these energy expressions.

Main Results:

  • It is shown that the local virial theorem (2K(r) = r·ΔV) can always be satisfied for any wave function and potential.
  • For each chosen local kinetic energy expression, an infinite number of quasi-probability distributions can be generated.
  • The local tensor virial theorem is also considered within this framework.

Conclusions:

  • The flexibility in defining local kinetic energy allows for the universal satisfaction of the local virial theorem.
  • Quasi-probability distributions offer a versatile tool for representing quantum mechanical systems under the local virial theorem.
  • The findings contribute to a deeper understanding of the local virial theorem and its implications in quantum chemistry and physics.