Gaussian积分 e(ikx)*e(-k‘x^2/2)积分区间无穷，积分变量x, k k'参数

显示全部楼层 · 2009-12-27 06:26:04

f(x)=e(-k′x^2/2)g(k)=∫e(ikx)e(-k′x^2/2)dx /*g(k)=∫e(ikx)f(x)dx*/df(x)/dx+k′xf(x)=0→∫e(ikx)(df(x)/dx+k′xf(x)=0)dx∫e(ikx)df(x)/dxdx=-ikg(k) /*by parts*/∫e(ikx)k′xf(x)=-ik′dg(k)/dk→kg(k)+k′dg(k)/dk=0→g(k)=Ce(-k^2/(2k′))where C=g(0)=∫e(-k′x^2/2)dx=√(2π/k′) /*Gaussian*/→g(k)=√(2π/k′)e(-k^2/(2k′))i.e. ∫e(ikx)e(-kx^2/2)dx=g(k)=√(2π/k′)e(-k^2/(2k′)) FOURIER TRANSFORM OF GAUSSIAN FUNCTION高斯函数的傅里叶变换~~~~~~~

千问 · 2009-12-27 06:26:04

您的id等级为什么那么高啊?