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// Scilab Code Ex 10.4 Degeneracy of Energy Level: Page-332 (2010)
// Function to find the factorial of a number
function[f] = fact(num)
f = 1;
for i = 1:1:num
f = f*i;
end
endfunction
// Fucntion to determine degenerate energy states
function[degstates] = degno(a, b, c)// degno takes three arguments
if a == b & b == c then // check if all the values are same
degeneracy = 3;
degstates = fact(3)/fact(degeneracy); //calculate degenerate states
end
if a == b | b == c | c == a then // check if any two values are equal
degeneracy = 2;
degstates = fact(3)/fact(degeneracy); //calculate degenerate states
end
if a ~= b & b ~= c then // check if all the values are different
degeneracy = 1;
degstates = fact(3)/fact(degeneracy); //calculate degenerate states
end
endfunction
//
clc
coef = 38; // Coefficient of H^2/(8*m*a^2)
nx = zeros(1,5); // Quantum number corresponding to x-direction
ny = zeros(1, 5); // Quantum number corresponding to y-direction
nz = zeros(1,5); // Quantum number corresponding to z-direction
deg = zeros(1,5); // Variable to store the degeneracy of states
count = 1; // set the counter
sum = 0; // initialize the sum
// Look for all the possible set of values for nx, ny and ny
for i = 1:1:10
for j = 1:1:10
for k = 1:1:10
// Check for the condition and avoid repetition of set of values
if ((i^2+j^2+k^2==coef) & (i+j+k)> sum) then
nx(1,count)=i; // Save current i value
ny(1,count)=j; // Save current j value
nz(1,count)=k; // Save current k value
deg(1,count) = degno(i, j, k); // Save degeneracy for given set of values
count = count + 1; // Increment the counter
sum = i + j + k; // Add the three values of quantum numbers
end
end
end
end
printf("\nThe %d set(s) of values of quantum number are : \n", count-1);
deg_states = 0; // Intialize the variable
for i = 1:1:count-1
printf("\nnx = %d, ny = %d, nz = %d\n", nx(1,i), ny(1,i), nz(1,i));
deg_states = deg_states + deg(1,i); // Accumulate the degeneracy
end
printf("\nThe given energy level is %d-fold degenerate.", deg_states);
//Result
// The 2 set(s) of values of quantum number are :
// nx = 1, ny = 1, nz = 6
// nx = 2, ny = 3, nz = 5
// The energy level is 9-fold degenerate
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