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 and See Chapter 3 page no. 19

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