Se for utilizar o material, favor citar como:

1)J.P. Braga e F.S. Carvalho - Métodos Numéricos em Química Quântica, 2021.
2)J.P. Braga, Fundamentos de Química Quântica, Editora UFV, 2007.

Problemas capítulo 9

%c9p1.m
clear all
M=[8 25 48;25 128 292;48 292 1920];
L=[54 208 348;208 1012 2048;348 2048 8592];
N=[32 140 192;140 768 1232;192 1232 4608]; 
fun = @(k) min(eig(k.^2*M-k.*L,N));kmin = fminsearch(fun,3);
en = fun(kmin)

% c9pg2.m
%dim = tamanho da base
%s^l1 t^m1 u^n1
%s^l2 t^m2 u^n2 
%... 
%s^lk t^mk u^nk
% Entrada do vetores l,m e n será:
%l=[l1 l2 ... lk],l=[m1 m2 ...mk],n=[n1 n2 ... nk]
%
clc, clear all, close all
Z=2;
%dim=1;l=[0];m=[0];n=[0];
%dim=2;l=[0 0];m=[0 0];n=[0 1];
dim=3;l= [0 0 0];m= [0 0 2];n= [0 1 0];
%dim=6;l=[0 0 0 1 2 0];m=[0 0 2 0 0 0];n=[0 1 0 0 0 2];
%dim=140;l=[0:1:3];m=[0:2:8];n=[0:1:6];
for i=1:dim,for j=1:dim
a0(i,j)=l(i)+l(j);a1(i,j)=l(i)+l(j)+1;a2(i,j)=l(i)+l(j)+2;
a3(i,j)=l(i)+l(j)-1;a4(i,j)=l(i)+l(j)-2;
b0(i,j)=m(i)+m(j);b1(i,j)=m(i)+m(j)+1;b2(i,j)=m(i)+m(j)+2;
b3(i,j)=m(i)+m(j)-1;b4(i,j)=m(i)+m(j)-2;
c0(i,j)=n(i)+n(j);c1(i,j)=n(i)+n(j)+1;c2(i,j)=n(i)+n(j)+2;
c3(i,j)=n(i)+n(j)-1;c4(i,j)=n(i)+n(j)-2;
end,end,	

% Matrizes M,L e N.
for i=1:dim,for j=1:dim,
M(i,j)=(l(i)*l(j)-m(i)*m(j)+l(i)*n(j)+n(i)*l(j)-m(i)*n(j)-...
m(j)*n(i))*fhyl(a0(i,j),b0(i,j),c1(i,j))-0.5*(l(i)+l(j)+...
n(i)+n(j))*fhyl(a1(i,j),b0(i,j),c1(i,j))-(n(i)*n(j)+l(i)*...
n(j)+n(i)*l(j))*fhyl(a0(i,j),b2(i,j),c3(i,j))+(n(i)*n(j)+...
m(i)*n(j)+m(j)*n(i))*fhyl(a2(i,j),b0(i,j),c3(i,j))+0.5*(l(i)...
+l(j))*fhyl(a3(i,j),b2(i,j),c1(i,j))+0.5*(n(i)+n(j))*...
fhyl(a1(i,j),b2(i,j),c3(i,j))-l(i)*l(j)*fhyl(a4(i,j),...
b2(i,j),c1(i,j))+m(i)*m(j)*fhyl(a2(i,j),b4(i,j),c1(i,j))+...
0.25*fhyl(a2(i,j),b0(i,j),c1(i,j))-0.25*fhyl(a0(i,j),...
b2(i,j),c1(i,j));
L(i,j)=4*Z*fhyl(a1(i,j),b0(i,j),c1(i,j))-fhyl(a2(i,j),...
b0(i,j),c0(i,j))+fhyl(a0(i,j),b2(i,j),c0(i,j));
N(i,j)=fhyl(a2(i,j),b0(i,j),c1(i,j))-fhyl(a0(i,j),...
b2(i,j),c1(i,j));
end,end

function f=fhyl(a,b,c)
f=factorial(a+b+c+2)/((b+1)*(b+c+2));

%c9pg3.m
format long
fun=@(k) min(eig(k.^2*M-k.*L,N));kmin = fminsearch(fun,3),
en=fun(kmin)