Solve the s-wave Schrodinger equation for ground state & first excited state of hydrogen atom using scilab(5th sem practical)

 

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CODING:

h=627.773
m=0.511e6
n=200
r0=1e-15
rm=10
e=3.795
r=linspace(r0,rm,n);
d=(rm-r0)/n
A=zeros(n,n)
V=zeros(n,n)
A(1,[1:2])=[-2,1];
A(n,[n-1:n])=[1,-2];
for i=2:n-1
    A(i,[i-1:i+1])=[1,-2,1]
end
for i=1:n
    V(i,i)=((e.^2)/r(i));
    V1(i)=(-(e.^2)/r(i));
end
H=((h.^2)/(2*m*d*d)*A)+V
[y,eig]=spec(H)
subplot(2,2,1)
for i=10:n
    plot(r(i),V1(i),'y+')
    xlabel("X-Axis")
    ylabel("Y-Axis")
end
disp(eig(n-1,n-1))
disp(eig(n-2,n-2))
disp(eig(n-2,n-2))
subplot(2,2,2)
plot(r,abs(y(:,n-2)),'b')
xlabel("X-Axis")
ylabel("Y-Axis")
subplot(2,2,4)

plot(r,abs(y(:,n-3)),'g')
xlabel("X-Axis")
ylabel("Y-Axis")
subplot(2,2,5)
legend('y,ground state n=1, y2 fes n=2,1,0')

OUTPUT:

Scilab Programming
C ++ Programming
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