_"I am using .^ but..."
But you aren't, everywhere. The line given by the error message is--
hq = @(q,n0) ((eq(q))^2+2*U*n0*(eq(q))).^0.5;
The term (eq(q))^2 doesn't have a 'dot' operator just as the error says.
BTW, do NOT use eq as a variable or function name; that aliases the builtin logical "equal" function == or eq()
>> which eq