### 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

### COMMON COLLECTOR CONFIGURATION OF A TRANSISTOR

COMMON COLLECTOR CONNECTION

In  this  configuration  the  input  is  applied  between the  base  and  the  collector and  the  output  is  taken  from  the  collector  and  the  emitter.  Here  the  collector  is common to both the input and the output circuits as shown in Fig.

Common Collector Transistor Circuit

In  common  collector  configuration  the  input  current  is  the  base current  IB  and  the output current is the emitter current IE. The ratio of change in emitter current to the  change in the base current is called current amplification factor.

It is represented by

COMMON COLLECTOR CIRCUIT

A test  circuit  for determining the  static characteristic  of an NPN transistor is shown in Fig. In this circuit the collector is common to both the input and the output circuits.   To   measure   the   base   and   the   emitter   currents,   milli   ammeters   are connected in series with the base and the emitter circuits. Voltmeters are connected   across the input an…