### 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 J

^{2}=Jx^{2}+ Jy^{2}+ Jz^{2}
Then we get

(Jm |

**J**^{2}|Jm)= (Jm |Jx^{2}|Jm) +(Jm |Jy^{2}|Jm)+ (Jm |Jz^{2}|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 J

for complete understanding download Solution Manual : Mathematical methods for physicists 5th edition Arfken and Weber and See Chapter 3 page no. 19 ^{2}=Jx^{2}+ Jy^{2}+ Jz^{2}are real and non negative
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