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Related Experiment Videos

Bound-state equivalent potentials with the Lagrange mesh method.

Fabien Buisseret1, Claude Semay

  • 1Groupe de Physique Nucléaire Théorique, Université de Mons-Hainaut, Académie universitaire Wallonie-Bruxelles, Place du Parc 20, BE-7000 Mons, Belgium. fabien.buisseret@umh.ac.be

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 16, 2007
PubMed
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The Lagrange mesh method accurately solves inverse eigenvalue problems, finding local potentials from wave functions and energies. This versatile technique works for both nonrelativistic and semirelativistic systems.

Area of Science:

  • Computational physics
  • Quantum mechanics
  • Theoretical chemistry

Background:

  • The Lagrange mesh method offers a straightforward approach to solving eigenvalue problems for two-body Hamiltonians.
  • Existing methods may face challenges with nonlocal potentials or relativistic kinematics.

Purpose of the Study:

  • To demonstrate the Lagrange mesh method's capability in solving the inverse eigenvalue problem.
  • To determine equivalent local potentials from given wave functions and energies.
  • To validate the method's efficacy across various physical systems and relativistic frameworks.

Main Methods:

  • Applying the Lagrange mesh method to inverse eigenvalue problems.
  • Utilizing analytically solvable cases for validation: nonrelativistic harmonic oscillator, Coulomb potential, nonlocal Yamaguchi potential, and semirelativistic harmonic oscillator.

Related Experiment Videos

  • Accurate computation of potentials from bound-state wave functions and energies.

    • Main Results:

    • The Lagrange mesh method successfully reconstructs local potentials for diverse systems.
    • The method accurately computes potentials for both nonrelativistic and semirelativistic cases.
    • Efficient handling of both local and nonlocal potentials is demonstrated.

    Conclusions:

    • The Lagrange mesh method is a powerful and versatile tool for solving inverse eigenvalue problems in quantum mechanics.
    • The approach provides accurate potential reconstruction for both relativistic and nonrelativistic kinematics.
    • This method simplifies the determination of equivalent local potentials, enhancing computational efficiency.