Operators and matrix elements in second-quantization representation

1997 ◽  
pp. 121-137
Keyword(s):  
Matrix Elements ◽  
Second Quantization ◽  
Quantization Representation

scholarly journals On a Unified Theory of Twocentre Harmonic Oscillator Integrals I. The Onedimensional Oscillator

1971 ◽  
Vol 26 (6) ◽  
pp. 940-942
Author(s):  
W . Wltschel
Keyword(s):  
Harmonic Oscillator ◽  
Collision Energy ◽  
Unified Theory ◽  
Overlap Integrals ◽  
Second Quantization ◽  
Quantization Representation ◽  
Franck Condon

Abstract Twocentre harmonic oscillator overlap integrals, arbitrary transition integrals and collision energy etchange integrals for equal and different frequencies of the oscillators are contained in a generalized Franck-Condon-integral which is solved by operator methods in the second quantization representation.

SOLVING THE SINGLE LAYER MULTICONFIGURATION TIME-DEPENDENT HARTREE–FOCK EQUATION IN SECOND QUANTIZATION REPRESENTATION BASED ON A DECOMPOSITION OF THE OVERALL FOCK SPACE

2013 ◽  
Vol 12 (01) ◽  
pp. 1250105 ◽  
Author(s):  
WENLIANG LI ◽  
X. WENWU ◽  
H. KELI
Keyword(s):  
Fock Space ◽  
Single Layer ◽  
Time Dependent ◽  
Initial Condition ◽  
Imaginary Time ◽  
Second Quantization ◽  
Hartree Fock ◽  
Time Propagation ◽  
Set Up ◽  
Quantization Representation

Very recently, the multilayer multiconfiguration time-dependent Hartree (MCTDH) method based on a decomposition of the overall Fock space in second quantization representation was proposed [Wang H, Thoss M, J Chem Phys131:024114, 2009], and they have presented demonstrative numerical example on vibrationally coupled electron transport. Followed by the thinking, the strategies of the implement of the theory to deal with multielectron dynamics with consideration coulomb interaction were discussed in detail. Some demonstrative calculations have been carried out by using the single layer MCTDHF method. The influences of the different choice way of initial condition, such as the species of basis function, the type of decomposition of the full Fock space, the choice of the spin orbitals, the number of the single particle function and so on, on the imaginary time propagation are mainly studied. The bridge between the generalized theory and the calculation application has been set up.

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