Bemerkung zur Rayleigh-Schr�dinger-St�rungstheorie

On a formal treatment of the Rayleigh-Schrödinger perturbation theory

“…The perturbation expressions formulated in this way provide insights into some of their interesting features as was illustrated by examples in [9] and [14] which indicate where this treatment of perturbation theory has advantages over the usual formulation. The formalism should be applied to further practical examples such as the calculation of multipole moments of compound systems.…”

“…If the spectrum of w(o) has no continuous part as was assumed in [9], the operator This vector satisfies the condition of normalization of Is) to unity in second order and fulfils the equation Im<s ~ I s2>=0. The example gives rise to consider the normalization and the specific structure of the eigenvector computed by means of our first-order iteration method.…”

“…In the non-degenerate case, the RS expressions for the n'th-order terms is") and E} ") can be constructed by the repeated application of r to the unperturbed terms If E} ~ is an eigenvalue of jr(o) with finite degeneracy, it was observed [9] that the operator ~, can be used to construct the RS projector ~s= Z, 2"~} ") whose zeroth order N~o) is the projector onto the subspace of Jt ~~ corresponding to E} ~ We have…”

“…For instance, the quantum mechanical expression for the electric polarizability can be calculated from the expression for the electric dipole moment, the expression for the hyperpolarizability from that for the polarizability etc. [9].…”

“…This was demonstrated by a simple proof of a linked cluster theorem [9,14] and the quantum mechanical adiabatic theorem [13]. In these applications, extensive formal calculations could be replaced by a direct conclusion.…”