Need help solving first order DiffyQ analytically with matrix

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Eva Carrillo
Eva Carrillo 2019-12-10
编辑： Ridwan Alam 2019-12-10
I'm given the equation . This can also be written as . Where where and is a 2x1 matrix with initial value of . I need to solve this problem analytically with Euler method, I've already solved it numerically. I need to plot time vs. intensity.
my code attempt is as follows:
gamma=0.5;
H=[(gamma*i) -1;-1 -i*gamma];
G=(2:2);
psi=(2:1);
psi(1,1)=1;
psi(2,1)=0;
T=10;
N=1000;
deltat=T/N;
x=[];
y=[];
t=[];
x(1)=0.5;
y(1)=0;
t(1)=0;
t1=[];
for t=1:N
t1(end+1)=t;
x(t+1)=x(t)+y(t)*deltat;
y(t+1)=y(t)+deltat*(-i*H*psi);
intensity=abs(y).^2;
int1(end+1)=intensity(1,1);
int2(end+1)=intensity(2,1);
end
plot (t1,int1,'-*');
hold on;
plot (t1,int2,'-*');
hold off;
I keep getting the error 'Unable to perform assignment because the left and right sides
have a different number of elements.' for line 36: y(n+1)=n*y(n)+deltat*(-i*H*psi);
I am very confused by this and could use the help!

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Ridwan Alam
Ridwan Alam 2019-12-10
编辑：Ridwan Alam 2019-12-10
If I understood it right, your x and y are supposed to be 2x1 vectors.
gamma=0.5;
H=[(gamma*i) -1;-1 -i*gamma];
% G=(2:2); % where is it used?
psi=zeros(2,1);
psi(1)=1;
psi(2)=0;
T=10;
N=1000;
deltat=T/N;
x1=0.5;
y1=0;
t=0;
x=[x1; x1];
y=[y1; y1];
t1=[]; int1 = []; int2 = [];
for t=1:N
t1(end+1)=t;
x(:,t+1)=x(:,t)+y(:,t)*deltat;
y(:,t+1)=y(:,t)+deltat*(-i*H*psi);
intensity=abs(y(:,t+1)).^2;
int1(end+1)=intensity(1);
int2(end+1)=intensity(2);
end
plot (t1,int1,'-*');
hold on;
plot (t1,int2,'-*');
hold off;
Hope this helps!

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