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  • Letter

Resolving the spurious-state problem in the Dirac equation with the finite-difference method

Ying Zhang

Yuxuan Bao and Hong Shen*

Jinniu Hu†

  • Department of Physics, School of Science, Tianjin University, Tianjin 300354, China

  • School of Physics, Nankai University, Tianjin 300071, China

  • School of Physics, Nankai University, Tianjin 300071, China and Shenzhen Research Institute of Nankai University, Shenzhen 518083, China

  • *songtc@nankai.edu.cn
  • †hujinniu@nankai.edu.cn
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Phys. Rev. C 106, L051303 – Published 18 November, 2022

DOI: https://doi.org/10.1103/PhysRevC.106.L051303

Abstract

To solve the Dirac equation with the finite-difference method, one has to face the spurious-state problem due to the fermion doubling problem when using the conventional central difference formula to calculate the first-order derivative on equal interval lattices. This problem is resolved by replacing the central difference formula with the asymmetric difference formula, i.e., the backward or forward difference formula. To guarantee the hermiticity of the Hamiltonian matrix, the backward and forward difference formula should be used alternatively according to the parity of the wave function. This provides a simple and efficient numerical prescription to solve various relativistic problems in the microscopic world.

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Phys. Rev. C 106, L051303– Published 18 November, 2022
  • Received 22 July 2022
  • Revised 1 November 2022
  • Accepted 8 November 2022
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