论文标题
通过有限差异方法在狄拉克方程中解决伪造的问题
Resolving the spurious-state problem in the Dirac equation with finite difference method
论文作者
论文摘要
为了使用有限差异方法求解狄拉克方程，由于使用常规的中央差异公式在相等的间隔晶格上计算一阶导数时，由于费米昂加倍问题，必须面对伪造的问题。通过用不对称差异公式（即后退或前向差异公式）代替中心差异公式来解决此问题。为了确保汉密尔顿矩阵的Hermitian，应根据波函数的奇偶校验或向后差的公式。这提供了一种简单有效的数值处方，可以解决微观世界中的各种相对论问题。
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.
