5. Diagonalization of a spin-1 operator. For a spin-1 system, Hilbert space is spanned by three basis vectors. We work i

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5 Diagonalization Of A Spin 1 Operator For A Spin 1 System Hilbert Space Is Spanned By Three Basis Vectors We Work I 1 (19.92 KiB) Viewed 155 times

5. Diagonalization of a spin-1 operator. For a spin-1 system, Hilbert space is spanned by three basis vectors. We work in S₂ representation. The eigenvalues of S₂ are +ħ, 0. and -ħ and the corresponding base kets are 11), 10), and 1-1). (a) Give S, in eigen representation in Dirac notation and the corresponding matrix representation. (b) Consider the observable given by A = -11X(1| +11X0-10X(1| + e|-1X(-1| where e is real. i. Verify that A is Hermitian.. ii. Find the eigenvalues and enkets of A.