Q. The matrices representing the angular momentum components jx jy jz are all hermitian .Show that the Eigen values of j2 is equal TO J2 =JX2 +JY2+JZ2 are REAL AND NON-NEGATIVE.

 Ans. This question is taken from the "Mathematical Methods for Physicist" Problem number 3.5 from chapter no 3

Finding the eigen values for J²=Jx² + Jy² + Jz²

Then we get

(Jm |J²|Jm)= (Jm |Jx²|Jm) +(Jm |Jy²|Jm)+ (Jm |Jz²|Jm)

Which can also be written as

|Jx(jm)|² + |Jy(jm)|² + |Jz(jm)|²

The above equation shows that the eigen values for J²=Jx² + Jy² + Jz² are real and non negative

   for complete understanding download Solution Manual : Mathematical methods for physicists 5th edition Arfken and Weber  and See Chapter 3 page no. 19