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this is my first time being here. I am a beginner learning some introductions on Bose-Einstein Condensation (BEC) on my own. Often times in the literature (say, [1], [2] (p.409) ) it comes theone-body(single-particle) density matrix, as

[tex]<\psi|\mathbf{\Psi(r)^\dagger\Psi(r')}|\psi>=N\int dx_2...dx_N~\psi^*(r,x_2,...,x_N)\psi(r',x_2',...,x_N')

[/tex]

I am not sure how to derive the above equation... My first step is to write [itex]<\psi|\mathbf{\Psi(r)^\dagger\Psi(r')}|\psi>[/itex] as

[tex]

<\psi|\mathbf{\Psi(r)^\dagger\Psi(r')}|\psi>=\int dx_1...dx_N \int dx_1'...dx_N' \psi_t^*(x_1,...,x_N)<x_1,...,x_N|\mathbf{\Psi(r)^\dagger\Psi(r')}|x_1',...,x_N'>\psi_t(x_1,...,x_N)

[/tex]

then I am not sure how to handle [itex]<x_1,...,x_N|\mathbf{\Psi(r)^\dagger\Psi(r')}|x_1',...,x_N'>[/itex]. Any ideas?

thanks in advance for help and comments,

C.H.

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# How BEC being described by the single-particle density matrix?

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