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Determination of a wave function functional.

Xiao-Yin Pan1, Viraht Sahni, Lou Massa

  • 1The Graduate School of the City University of New York, New York, New York 10016, USA.

Physical Review Letters
|November 5, 2004
PubMed
Summary
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This study introduces a new variational method, treating wave functions as functionals of other functions. This approach enables constrained searches for energy upper bounds in quantum mechanics.

Area of Science:

  • Quantum mechanics
  • Computational chemistry
  • Theoretical physics

Background:

  • Traditional variational methods in quantum mechanics treat wave functions as simple functions.
  • This limits the scope of accessible wave function representations and potential energy calculations.

Purpose of the Study:

  • To propose an expansion of the variational principle in quantum mechanics.
  • To introduce a novel approach for calculating energy by treating wave functions as functionals.
  • To demonstrate a rigorous construction of this new method.

Main Methods:

  • The wave function (psi) is redefined as a functional of a set of functions (chi): psi = psi[chi].
  • A constrained search is performed over all functions chi.
  • This search ensures the functional psi[chi] satisfies a sum rule or yields a physical observable.

Related Experiment Videos

  • Variational minimization is used to obtain an upper bound to the energy.

    • Main Results:

    • An upper bound to the energy is obtained through variational minimization.
    • The method rigorously constructs a constrained-search-variational wave function functional.
    • This expands the possibilities within variational calculations.

    Conclusions:

    • The proposed functional approach offers a more flexible and potentially more accurate method for variational calculations.
    • This work demonstrates the feasibility and rigor of constructing such wave function functionals.
    • The method opens new avenues for theoretical and computational studies in quantum mechanics.