  To solve the Dirac equation with the finite difference method, one has to
face up to the spurious-state problem due to the fermion doubling problem when
using the conventional central difference formula to calculate the first-order
derivative on the 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
hermitian of the Hamiltonian matrix, the backward and forward difference
formula should be used alternatively according to the parity of the
wavefunction. This provides a simple and efficient numerical prescription to
solve various relativistic problems in the microscopic world.
