Overlap integrals and single-particle wave functions in direct interaction theories

1965 ◽  
Vol 72 (2) ◽  
pp. 337-351 ◽  
Author(s):  
Tore Berggren
Keyword(s):  
Single Particle ◽  
Direct Interaction ◽  
Wave Functions ◽  
Overlap Integrals

scholarly journals Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 408
Author(s):  
Matteo Villani ◽  
Guillermo Albareda ◽  
Carlos Destefani ◽  
Xavier Cartoixà ◽  
Xavier Oriols
Keyword(s):  
Single Particle ◽  
Degrees Of Freedom ◽  
Single Photon ◽  
Open Quantum Systems ◽  
Wave Functions ◽  
Practical Application ◽  
Light Matter Interaction ◽  
Pure States ◽  
Energy And Momentum ◽  
Full Quantum

Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWFs) allow for a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of single-particle time-dependent pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light–matter interaction phenomena in a resonant tunneling device, where a single photon interacts with a single electron. Third, we emphasize the importance of interpreting such a scattering mechanism as a transition between initial and final single-particle BCWF with well-defined central energies (rather than with well-defined central momenta).

Single-Particle Resonant-State Wave Functions in a Simple Description of Isobaric Analog Resonances

1970 ◽  
Vol 1 (1) ◽  
pp. 1-3 ◽  
Author(s):  
B. Gyarmati ◽  
T. Vertse ◽  
J. Zimányi ◽  
M. Zimányi
Keyword(s):  
Single Particle ◽  
Resonant State ◽  
Wave Functions ◽  
Simple Description ◽  
State Wave ◽  
Isobaric Analog

On the computation of matrix elements between arbitrary single-particle wave functions

1980 ◽  
Vol 339 (1) ◽  
pp. 1-12 ◽  
Author(s):  
P. Desgrolard ◽  
W. Glöckle ◽  
J. Le Tourneux
Keyword(s):  
Single Particle ◽  
Wave Functions ◽  
Matrix Elements

One-dimensional overlap functions and their application to Auger recombination in semiconductors

1960 ◽  
Vol 258 (1295) ◽  
pp. 486-495 ◽  
Keyword(s):  
Auger Recombination ◽  
Elevated Temperatures ◽  
Bloch Wave ◽  
Wave Functions ◽  
General Analysis ◽  
Experimental Results ◽  
Overlap Integrals ◽  
Recombination Mechanism ◽  
One Dimensional ◽  
Good Agreement

The theoretical lifetime of excess carriers in semiconductors limited only by the Auger recombination mechanism previously discussed by the present authors, depends on a temperature-independent parameter. This involves certain overlap integrals. They are of the form ∫ u *(k 1 , r) u (k 2 , r) dr, where the u ’s are the modulating parts of Bloch wave functions. The integrals are calculated in this paper on the basis of a Kronig-Penney model. The value of the parameter obtained is shown to be rather insensitive to many details of the model used. When the value found is inserted into the previously published theory of lifetimes in InSb, very good agreement is obtained with the more detailed experimental results which have recently become available. This strongly suggests that the dominant recombination mechanism in InSb at elevated temperatures has been identified. A more general analysis of the properties of the overlap integrals is also given in this paper.

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