2
votes
3answers
94 views

Proof for a time-ordering equation in Negele & Orland (1998)

Let $T$ be the time-ordering operator which orders operators $A_1(t_1), A_2(t_2), \ldots$ such that the time parameter decreases from left to right: $$T[A_1(t_1) A_2(t_2)] = A_2(t_2) A_1(t_1) \text{ ...
2
votes
0answers
73 views

Is time ordering defined for a single operator depending of two time variables?

The time ordering for the purpose of quantum mechanics is e.g. given by $${\mathcal T} \left[A(x) B(y)\right] := \begin{matrix} A(x) B(y) & \textrm{ if } & x_0 > y_0 \\ \pm B(y)A(x) & ...
6
votes
2answers
353 views

“Correlation energy” using the pair correlation function

In this paper on the Quantum Hall effect the authors refer to something called the correlation energy of electrons. It is defined at the top of page 5 as $E=\frac{n}{2}\int (g(r)-1)V(r)dA\ ,$ where ...
1
vote
0answers
103 views

Equal time displacement correlation functions and their physical interpretation?

Displacement correlation functions in question are within harmonic approximation and are derived for example in: A. Maradudin, Dynamical properties of solids 1, 1 (1974). Maradudin says about the ...
6
votes
1answer
254 views

Differential equation (Greens function) satisfied by the kernel using path integrals

I'm reading Feynman and Hibbs, Quantum Mechanics and Path Integrals. How do I show that the kernel $$\tag{2-25} K(x_2 t_2;x_1 t_1)=\int e^{\frac{i}{\hbar}S[2,1]}\mathcal{D}x$$ satisfies the ...
1
vote
2answers
146 views

$\langle B|A \rangle$ expressed in terms of the Partition Function

Say you have an electron departing from point A and reaching poing B after a time t. According to some helping friend, the Partition Function for that electron going from point A to B can be written ...
5
votes
2answers
247 views

Correlation, Time Ordering, and Observables

In general, the product of two Hermitian operators $\phi$ will not be Hermitian, unless the two operators commute. Question: is $X = T \phi(t_1) \phi(t_2)$ Hermitian? It doesn't seem to be if $T ...
4
votes
1answer
355 views

How would Kohn-Sham orbitals differ from 'true' elecron wavefunctions?

How would the non-interacting electron orbitals from a perfect DFT solution for a given potential shape differ from the 'true' electron wavefunctions? Or can you only really talk about the total ...