On the Löwdin Bracketing Function

Abstract

In his series of publications “studies in perturbation theory”, /1–2/ Löwdin introduced the bracketing function

$$f(z) = < \phi \left| {H + HT(Z)H} \right|\phi >$$

(1)

where H is the Hamiltonian, φ the reference function belonging to the Hilbert space h and T the reduced resolvent

$$T(z) = P{({z^{ - PHP}})^{ - 1}}P$$

(2)

$$p = 1 - 0;{\kern 1pt} 0 = \left| {\phi >< \phi } \right|;{\kern 1pt} < \left. \phi \right|\phi >= 1.$$

(3)