The Seke self-consistent projection-operator approach for the calculation of quantum-mechanical eigenvalues and eigenstates

J. Seke, A.V. Soldatov and N.N. Bogolubov

Physica A: Statistical Mechanics and its Applications, 1997, vol. 246, issue 1, 221-240

Abstract: Originally, the Seke self-consistent projection-operator method has been developed for treating non-Markovian time evolution of probability amplitudes of a relevant set of state vectors. In the so-called Born approximation the method leads automatically to an Hamiltonian restricted to a subspace and thus enables the construction of effective Hamiltonians. In the present paper, in order to explain the efficiency of Seke's method its algebraic operator structure is analyzed and a new successive approximation technique for the calculation of eigenstates and eigenvalues of an arbitrary quantum-mechanical system is developed. Since, unlike most perturbative techniques, in the present approach a well-defined effective (restricted) Hamiltonian in each order of the applied approximation exists, the self-consistency of all obtained results is self-evident. Finally, to illustrate the efficiency of the developed formalism, the optical polaron model is investigated.

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:246:y:1997:i:1:p:221-240

DOI: 10.1016/S0378-4371(97)00344-0

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