numerov3.m

求解量子力学的薛定谔方程

function f=numerov3(x0,x1,N,P,W,E,Y0,DY0);
%> The file <numerov3.m> integrates the 1D Schrodinger equation 
%> for an 'arbitrary' potential using the Numerov method.
%> IT IS JUST A MODIFICATION OF NUMEROV1 WITH SMALLER DEMAND ON MEMORY
%> (by avoiding the creation of large matrices).
%> It also allows the potential to be a function of a parameter.
%> It produces the function values and derivatives at the second end 
%> point as a function of energy (to satisfy boundary condition),
%> it does not keep the solution function.
%> Call: numerov3(x0,x1,N,'pot(X,W)',W,E,Y0,DY0);
%> (x0,x1) = end points of integration interval.
%> N = number of steps (N subintervals of length h).
%> P = 'pot(X,W)' if the potential function is stored in <pot.m>.
%> We can let P be a row vector (size E) for each X!
%> W = parameter as a row vector.
%> E = energy lattice as a row vector, same size as W.
%> Y0,DY0 = starting values in x0 , row vectors length(W).
%> Output: f = [Y;DY] = final values of function and derivative in x1,
%> size = [2,length(E)];
%>
%>