Off diagonal element of density matrix

  • Thread starter KFC
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  • #1
KFC
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Main Question or Discussion Point

For two level system , let denotes the ground state as 1 and exctied state as 2, for writing the office off-diagonal matrix element for the density operator, shall it be

[tex]\rho_{12} = |2\rangle\langle 1|[/tex]

and

[tex]\rho_{21} = |1\rangle\langle 2|[/tex]

???
 

Answers and Replies

  • #2
naima
Gold Member
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From a pure state f = a|0> + b|1> one gets the density opérator
(a|0> + b|1>)(a*<0| + b*<1|)
with a off diagonal part ab*|0><1|
the off diagonal matrix element is ab* = <f |0><1|f> (with |0> and |1> orthogonal)
With a mixture of pure state f1,f2 with probabilities p1, p2
we get p1<f1 |0><1|f1> + p2<f2 |0><1|f2>
I hope there is no error in my answer!
 

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