By Alexandru Popa
Quantum and Classical Connections in Modeling Atomic, Molecular and Electrodynamic platforms is meant for scientists and graduate scholars attracted to the principles of quantum mechanics and utilized scientists attracted to actual atomic and molecular types. this can be a connection with these operating within the new box of relativistic optics, in issues regarding relativistic interactions among very severe laser beams and debris, and is predicated on 30 years of analysis. the newness of this paintings involves exact connections among the houses of quantum equations and corresponding classical equations used to calculate the lively values and the symmetry houses of atomic, molecular and electrodynamical platforms, in addition to providing functions utilizing tools for calculating the symmetry homes and the lively values of platforms and the calculation of houses of excessive harmonics in interactions among very extreme electromagnetic fields and electrons.
- Features precise causes of the theories of atomic and molecular platforms, in addition to wave houses of desk bound atomic and molecular systems
- Provides periodic suggestions of classical equations, semi-classical equipment, and theories of platforms composed of very excessive electromagnetic fields and debris
- Offers types and strategies in line with 30 years of research
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Additional info for Theory of Quantum and Classical Connections in Modeling Atomic, Molecular and Electrodynamical Systems
2A). 137) with b. 3A). 137) remain valid. 3 Components of the laser field in the S and S0 systems. The incident field has the πL polarization. The intensities of electric fields, the magnetic induction vectors, and the wave vectors, for incident and scattered fields, are shown on figures. The 180 and 90 geometries, in which the two beams collide, respectively, head-on and perpendicularly, are particular cases. These cases, correspond, respectively, to θL 5 0 and θL 5 6 90, for both, σL and πL polarizations.
151), respectively, by β 0x0 , and β 0z0 . 140), we have From Eqs. ðk 0Ly0 =jk 0L jÞdγ0 =dt0 . 0 β 0y0 5 k0Ly0 jk 0L j 12 1 γ0 Similarly, from Eqs. 155) The differentiation of the phase η0 , given by Eq. 143), leads to: ! 156), we obtain dðγ 0 β 0x0 Þ=dt0 5 2a cos η0 dη0 =dt0 . 157) We substitute the expressions of β 0x0 , β 0y0 , and β 0z0 , respectively, from Eqs. 158) From Eqs. 158) and, respectively, from Eqs. 158), we obtain the expressions of β 0y0 and β 0z0 . 160) β 0z0 5 From Eq. 149), we obtain β_ 0x0 " !
1 The σL Polarization. 2). Since our analysis is performed in the S0 system, we have to calculate the parameters of the laser field, denoted by E 0L , B0L , k 0L , and ω0L , in the S0 system. The four-dimensional wave vectors are denoted, respectively, by ðωL =c; kLx kLy ; kLz Þ and ðω0L =c; k0Lx0 ; k0Ly0 ; k 0Lz0 Þ in the systems S and S0 . 142) where β 0 and γ 0 are given by Eq. 61). 143) Since the relations between the spaceÀtime four-dimensional vectors in the systems S and S0 are ct0 5 γ0 ðct 1 jβ 0 jzÞ, x0 5 x, y0 5 y, and z0 5 γ 0 ðz 1 jβ 0 jctÞ, it is easy to see that these relations and Eqs.
Theory of Quantum and Classical Connections in Modeling Atomic, Molecular and Electrodynamical Systems by Alexandru Popa