AIM-Solve the s-wave radial Schrodinger equation for a particle of mass m: For the anharmonic oscillator potential for the ground state energy (in MeV) of particle to an accuracy of three significant digits. Also, plot the corresponding wave function. Choose m = 940 MeV/c2, k = 100 MeV fm-2, b = 0, 10, 30 MeV fm-3In these units, cħ = 197.3 MeV fm. The ground state energy I expected to lie between 90 and 110 MeV for all three cases.

 APPARATUS- sci lab 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.Dispaly the ground state energy for three value 0,10,3

INPUT-

h=197.3

m=940

k=100

b=0

n=100

r0=-5e-15

rm=5

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)=(0.5*k*r(i)*r(i)+0.3*b*r(i)*r(i)*r(i))

v1(i)=(0.5*k*r(i)*r(i)+0.3*b*r(i)*r(i)*r(i))

end

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

[y,eig]=spec(H)

subplot(2,2,1)

for i=1:n

plot(r(i),v1(i),'r+')

xlabel("X-AXIS")

ylabel("Y-AXIS")

end

disp(eig(1,1))

disp(eig(2,2))

disp(eig(3,3))

subplot(2,2,2)

plot(r,y(:,1)','r')

xlabel("X-AXIS")

ylabel("Y-AXIS")

subplot(2,2,3)

plot(r,y(:,2)','b')

xlabel("X-AXIS")

ylabel("Y-AXIS")

subplot(2,2,4)

plot(r,y(:,3)','g')

xlabel("X-AXIS")

ylabel("Y-AXIS")

OUTPUT-

for b=0;

1. 92.969987 (ground state energy)

2. 220.52532

3. 348.52647

for b=10

1. 96.080573 (ground state energy)

2. 231.55534

3. 370.15555

for b=30

1. 101.68673 (ground state energy)

2. 250.72637

3. 406.79431