A continued fraction representation of the mass operator

1976 ◽  
Vol 54 (1) ◽  
pp. 26-33 ◽  
Author(s):  
Dipak K. Saraswati
Keyword(s):  
Projection Operator ◽  
Continued Fraction ◽  
Mass Operator ◽  
Quantum Statistical Mechanics ◽  
Operator Method ◽  
Polarization Operator ◽  
First Approximation ◽  
Random Forces ◽  
Projection Operator Method ◽  
Quantum Statistical

We explore some further possibilities of application of the projection operator method of Zwanzig to the theory of Green's functions of quantum statistical mechanics, initiated by lchiyanagi, and present a continued fraction representation of the mass operator involving a hierarchy of the random forces. As an application of the theory, we calculate the polarization operator of the phonon Green's function of the Frohlich Hamiltonian in the first approximation which corresponds to the assumption that the electron momenta are orthogonal to the phonon momentum.

Novel Technique for Quantum-Mechanical Eigenstate and Eigenvalue Calculations based on Seke's Self-Consistent Projection-Operator Method

1997 ◽  
Vol 11 (06) ◽  
pp. 245-258 ◽  
Author(s):  
J. Seke ◽  
A. V. Soldatov ◽  
N. N. Bogolubov
Keyword(s):  
Projection Operator ◽  
Equations Of Motion ◽  
Operator Method ◽  
Approximation Order ◽  
Quantum Mechanical ◽  
Approximation Technique ◽  
Operator Structure ◽  
Projection Operator Method ◽  
Self Consistent ◽  
Effective Hamiltonians

Seke's self-consistent projection-operator method has been developed for deriving non-Markovian equations of motion for probability amplitudes of a relevant set of state vectors. This method, in a Born-like approximation, 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 in particular applications, 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. Unlike most perturbative techniques, in the present case each order of the approximation determines its own effective (approximating) Hamiltonian ensuring self-consistency and formal exactness of all results in the corresponding approximation order.

ERRATA: "PHOTOFIELD EMISSION CALCULATIONS BY USING PROJECTION OPERATOR METHOD"

2007 ◽  
Vol 21 (24) ◽  
pp. 1651-1652
Author(s):  
R. K. THAPA ◽  
M. P. GHIMIRE ◽  
GUNAKAR DAS ◽  
S. R. GURUNG ◽  
B. I. SHARMA ◽  
...  
Keyword(s):  
Projection Operator ◽  
Operator Method ◽  
Projection Operator Method
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