By Alexandru Popa
Quantum and Classical Connections in Modeling Atomic, Molecular and Electrodynamic structures is meant for scientists and graduate scholars drawn to the rules of quantum mechanics and utilized scientists drawn to exact atomic and molecular versions. it is a connection with these operating within the new box of relativistic optics, in issues on the topic of relativistic interactions among very excessive laser beams and debris, and relies on 30 years of study. the newness of this paintings includes actual 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 structures, in addition to providing functions utilizing tools for calculating the symmetry homes and the vigorous values of structures and the calculation of homes of excessive harmonics in interactions among very severe electromagnetic fields and electrons.
- Features distinctive factors of the theories of atomic and molecular platforms, in addition to wave houses of desk bound atomic and molecular systems
- Provides periodic recommendations of classical equations, semi-classical equipment, and theories of structures composed of very extreme electromagnetic fields and debris
- Offers versions and techniques according to 30 years of research
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Additional resources for Theory of Quantum and Classical Connections In Modeling Atomic, Molecular And Electrodynamical Systems
Finally, from Eqs. 36) it follows, respectively, that β x , β y , β z , β_ x , β_ y , and β_ z are periodic functions of only one variable, η. 37) where R is the distance from the electron to the observation point (the detector) and n is the versor of the direction electron detector. Connection Between KleinÀGordon and Relativistic HamiltonÀJacobi Equations 31 In virtue of the significance of the quantities entering in the LiènardÀWiechert equation, it results that the field E corresponds to the time t 1 R=c and we have E 5 Eðr 1 Rn; t 1 R=cÞ, where r is the position vector of the electron with respect to a system having its origin at the point defined by Eq.
111) Taking into account Eqs. 113) Taking into account Eqs. 114) We prove the following property which will be useful for the calculation of the intensities of the harmonic radiation beams in the S system. 116) where E 0j and E j are the intensities of the electric field and I 0 j and I j are the beam intensities, corresponding to the j harmonics, in the S0 and S systems. 117) Since from Eqs. 96), we have E 0j Á n0 5 0 and cB0j 5 n0 3 E 0j , and E 0j Á ½β 0 3 ðn0 3 E 0j Þ 5 E j02 ðβ 0 Á n0 Þ, Eq.
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 " ! 161) From Eqs. 155), we obtain k0Ly0 β 0y0 1 k0Lz0 β 0z0 5 Introducing this expression in Eq.