- #1
jajabinker
- 8
- 1
Hey guys!
In an n-electron system,
The second order reduced DM is defined as
[tex]\Gamma (x_{1},x_{2}) = \frac{N(N-1)}{2}\int{\psi(x_{1},x_{2}...,x_{n})\psi^{*}(x_{1},x_{2}...,x_{n})}dx_{3}...dx_{n}[/tex]
It can be intepreted as the probability of finding two electrons at [itex]x_{1}[/itex] and [itex]x_{2}[/itex] respectively for all possible configurations of the other electrons because of the probabilistic interpretation of [itex]|\psi\psi*[/itex]
The single particle density matrix is defined as :
[tex]\gamma (x_{1},x'_{1}) = N\int{\psi(x_{1},x_{2}...,x_{n})\psi^{*}(x'_{1},x_{2}...,x_{n})}dx_{2}...dx_{n}[/tex]
Where the prime variable appears only in the complex conjugate of the function.
Can this be interpreted in probabilistic terms? why is there a prime? What is the meaning of the product of a wave function with its complex conjugate and having a different variable.
I know that for the diagonal terms it reduces to [itex]\rho (r)[/itex].
Any replies are much appreciated.
In an n-electron system,
The second order reduced DM is defined as
[tex]\Gamma (x_{1},x_{2}) = \frac{N(N-1)}{2}\int{\psi(x_{1},x_{2}...,x_{n})\psi^{*}(x_{1},x_{2}...,x_{n})}dx_{3}...dx_{n}[/tex]
It can be intepreted as the probability of finding two electrons at [itex]x_{1}[/itex] and [itex]x_{2}[/itex] respectively for all possible configurations of the other electrons because of the probabilistic interpretation of [itex]|\psi\psi*[/itex]
The single particle density matrix is defined as :
[tex]\gamma (x_{1},x'_{1}) = N\int{\psi(x_{1},x_{2}...,x_{n})\psi^{*}(x'_{1},x_{2}...,x_{n})}dx_{2}...dx_{n}[/tex]
Where the prime variable appears only in the complex conjugate of the function.
Can this be interpreted in probabilistic terms? why is there a prime? What is the meaning of the product of a wave function with its complex conjugate and having a different variable.
I know that for the diagonal terms it reduces to [itex]\rho (r)[/itex].
Any replies are much appreciated.