The spin coherent states are defined in terms of the Fock states as 2j 2j la,....

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The spin coherent states are defined in terms of the Fock states as 2j 2j la,. a"|n) j= 0, 5,1, .. %3D n=0 1) Determine the normalization constant N. 2) Evaluate the expectation value of the operator ata with respect to |a, j). Hint: (:)- 2j! n!(2j – n)! 2j 2j 2j Σ( la1an = (1+ |a*)* n=0 2j Σ 1) 2j E laparn = 2;j|la° (1 + |a{*)i-1 n=0 [a, a*] = I %3D aln) = Vn]n – 1), at|n) = Vn + 1|n +1), ataln) = n|n). %3D 1/2 The spin coherent states are defined in terms of the Fock states as 2j 2j la,. a"|n) j= 0, 5,1, .. %3D n=0 1) Determine the normalization constant N. 2) Evaluate the expectation value of the operator ata with respect to |a, j). Hint: (:)- 2j! n!(2j – n)! 2j 2j 2j Σ( la1an = (1+ |a*)* n=0 2j Σ 1) 2j E laparn = 2;j|la° (1 + |a{*)i-1 n=0 [a, a*] = I %3D aln) = Vn]n – 1), at|n) = Vn + 1|n +1), ataln) = n|n). %3D 1/2