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ANALYTIC PROPERTIES OF PHYSICAL QUANTITIES
ESTIMATES IN ATOMIC MECHANICS
ESTIMATES IN QUANTUM ELECTRODYNAMICS
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analytic continuation applicability assume asymptotic form asymptotic series atomic electrons boundary conditions bremsstrahlung chapter charge exchange classical mechanics coefficient coincides collision Consequently coordinate correspondence principle corresponds Coulomb potential decreasing exponential determined dimensional distance electromagnetic field emission emitted electron energy levels equal to zero exact solution excitation exponentially small expression follows formula frequency Hamiltonian Hence hydrogen atom impact parameter incident particle integral integrand interaction ionization potential Lamb shift Let us consider Let us estimate Let us find molecule momentum motion necessary notation nucleus null vibrations number of nodes obtained order of magnitude oscillator perturbation theory phase probability problem proton quantization condition quantum mechanics quantum numbers quasi-classical approximation quasi-classical solution radial radius real axis region relationship saddle point scattering amplitude scattering angle scattering cross section Schrodinger equation shells singular point slow subsystem speed spherical steepest descent symmetrical tion transition values variable vector wave function