السلام عليكم
ارجو منكم التكرم بحل هذه الاسئلة جزاكم خير
الاول :
evaluate the commutators [ A,B] ,[B,C] ,[ C,A] for the operators
A=k sin 0-i cos 0 d/d0 , B= k cos 0+ i sin 0 d/d0 , C = - i d/d0
الثاني
The orthonormal functions yr (q) , - ∞ < q < ∞ , are such Qyr (q) =√((r+1)/2 ) y_(r+1 ) (q)+ √((2r))yr-1(q
And
d/(dq ) y_(r ) (q)= √((2r) ) y_(r-1 ) (q)-y_r (q
If for any function f(q) the operators Q and D are such that Qf(q) = qf(q) and
Df(q)= d/dq f(q) , find the matrix representations of these operators relative to the yr (q) as basic functions , and hence show that [ D,Q ] =I