Register to reply

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

Share this thread:
Jul21-14, 06:10 AM
P: 1
Hello everybody,

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 the one-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')

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

<\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)

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,
Phys.Org News Partner Physics news on
'Squid skin' metamaterials project yields vivid color display
Scientists control surface tension to manipulate liquid metals (w/ Video)
Simulation method identifies materials for better batteries
Jul21-14, 07:57 AM
Sci Advisor
P: 3,626
You probably know that e.g. ##\mathbf{\Psi(x_1)\Psi(x_2)}|0>=|x_1,x_2>## and so on for the position eigenstates of n particles in genera. Furthermore, you know the commutation properties of the Psi operators, ##\{\mathbf{\Psi^+(x_1),\Psi(x_2)}\}=\delta(x_1-x_2)##. This should be sufficient to work out the matrix element.

Register to reply

Related Discussions
Single particle single slit interference - question about the experiment Quantum Physics 6
Single slit single particle interference Quantum Physics 8
Conditions for a density matrix; constructing a density matrix Introductory Physics Homework 5
The single particle density of states (Statistical physics) Advanced Physics Homework 1
Is there any approximation to the two particle density matrix Quantum Physics 7