Aim-Solve the s-wave radial Schrodinger equation for an atom: where m is the reduced mass of the system (which can be chosen to be the mass of an electron), for the screened coulomb potential

 Find the energy (in eV) of the ground state of the atom to an accuracy of

three

significant digits. Also, plot the corresponding wavefunction. Take e =

3.795

(eVÅ)1/2, m = 0.511x106 eV/c2, and a = 3 Å, 5 Å, 7 Å. In these units ħc

= 1973

(eVÅ). The ground state energy is expected to be above -12 eV in all

three cases.

Apparatus- scilab software,Laptop .

Algorithm-

1. Write the all given values of h,m,n,r0,e .

2.Use the linspace command .

3. Give the matrix of ‘A’and ‘V’ .

4. Using the for loop .

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

6. write the equation of ‘H’ .

7. Using the ‘spec(H)’ command for eigen value .

8.Using the ‘subplot’ command and plot the potential graph

and other three graphs.

9. Using the ‘legend’ command .

10.Give the display command and show the ‘eigen value’ .

INPUT - 2

a=3,5,7

h=1973

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

V1(i)=(-(e.^2)/r(i))*(exp(-r(i)/a));

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-3,n-3))

subplot(2,2,2)

plot(r,abs(y(:,n-1)),'r')

xlabel("X-AXIS")

ylabel("Y-AXIS")

subplot(2,2,3)

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 first n=2,l=0')

OUTPUT – 2

EIGEN VALUES-*for a=3, *for a=7,

1. 9.22776 1. 11.503524

2. 0.4609445 2. 1.7146218

3. - 0.9688559 3. - 0.1459806

*for a=5,

1. 10.784776

2. 1.2427585

3. - 0.4712703