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