Aim:- To solve the s-wave radial schrodinger equation for the vibrations of Hydrogen molecule.. where is the reduced mass of thr two atom system for the morse potential Find the lowest vibrational energy (in MeV) of the molecule to an accuracy of three digits. Also plot the corresponding wave function. Take , m=940x106 eV/C2 D=0.755501 eV α=1.44 r0=0.131349 Å

 Apparatus:- a laptop with installed scilab

Algorithm:-

1. Put all the given constants(eg.- h,m,n,r0,e)

2. Use linspace command for linearly spaced vectors

3. give the zero matrix of 'A' and 'v'.

4. apply the loop.

5. write the equation of v(i,i).

6. write the equation of H.

7. find the eigen value using 'spec(H)' command.

8. plot the potential graph.

9.show the eigen value by 'disp()' command.

Program:-

clc;

clear()

clf()

h=197.3;

m=940;

d=0.755501

k=100;

b=0;

a=1.44

q0=3.795

r0=0.131349;

rm=10;

n=500;

r=linspace(r0,rm,n)

d=(r-r0)/r

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)=d*((exp(-2*a*(r(i)-r0)/r(i))))

-exp(-a*(r(i)-r0)/r(i))

end

H=-(((h^2)/(2*m*d*d))*A)+v;

[R,y]=spec(H)

w=find(H>>0.0)

disp(H(w(1)))

disp(y(3,3))

disp("energy first exited state=")

disp(H(w(2)))

R(1,:)=R(:,1)'

R(2,:)=R(:,2)'

plot(r,(R(1,:)),'red')

plot(r,(R(2,:)),'green')

xgrid()

output:-

energy first exited state=

0.0080949