理论物理中的虚时演化法.pdf

The equation @q 1 @2q 2 i @z = 2 @x2 pR (x) q jq j q; By employing image-time transformation z ! iz; one can Önd that it can be reduced to the following equation @q 1 @2q 2 @z = 2 @x2 + pR (x) q + jq j q; We begin by discretizing the domain x 2 [a; a] by placing a grid over the domain. We will use the grid with grid spacing h = 2a=N in r: Therefore, ri = a + (i 1) h (i = 1; 2; ; N + 1) : We also discretizing the domain z 2 [0; b] by placing a grid over the domain for d = b=M in z: Therefore, zj = (j 1) d (j = 1; 2; ; M + 1) : One can get the following di§erence scheme j +1 j j +1 j +1 j +1 q q 1 q + q 2q 2 i i = i+1 i1 i + pR qj +1 + qj qj +1 d 2 h2 i i i i namely j q 1 1 1 2 1 i = qj +1 + + pR qj qj +1 qj +1 d 2h2 i1 h2 d i i i 2h2 i+1 By setting 1 L = 2h2 j qi Qi = d 1 1 2