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Semirelativistic Lagrange mesh calculations.

C Semay1, D Baye, M Hesse

  • 1Université de Mons-Hainaut, Place du Parc, 20, B-7000 Mons, Belgium.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 20, 2001
PubMed
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The Lagrange mesh method accurately computes eigenvalues for nonrelativistic and semirelativistic Hamiltonians. This powerful computational technique is simple, fast, and easy to implement for quantum mechanics problems.

Area of Science:

  • Computational Quantum Chemistry
  • Theoretical Physics
  • Numerical Methods

Background:

  • The Lagrange mesh method is a robust technique for solving quantum mechanical eigenvalue problems.
  • Accurate computation of eigenvalues and eigenfunctions is crucial for understanding atomic and molecular systems.

Purpose of the Study:

  • To demonstrate the applicability and effectiveness of the Lagrange mesh method for semirelativistic two-body eigenvalue equations.
  • To evaluate the accuracy, speed, and simplicity of implementation for this method in a semirelativistic context.

Main Methods:

  • Developing trial eigenstates in a basis of well-chosen functions.
  • Computing Hamiltonian matrix elements by evaluating the potential at grid points.
  • Applying the Lagrange mesh method to solve semirelativistic two-body eigenvalue equations.

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Main Results:

  • The Lagrange mesh method proves effective for semirelativistic two-body eigenvalue equations.
  • The method achieves high accuracy, comparable to the nonrelativistic case.
  • The implementation is demonstrated to be fast and straightforward.

Conclusions:

  • The Lagrange mesh method is a versatile and powerful tool for both nonrelativistic and semirelativistic eigenvalue problems.
  • Its efficiency and simplicity make it suitable for various quantum mechanical computations.