By Eugene Oks

The booklet offers counterintuitive theoretical effects, which have been released in respected refereed journals through the book's writer and via others. those primary effects holiday numerous paradigms of quantum mechanics and supply substitute interpretations of a few vital phenomena in atomic and molecular physics. First, it really is proven that singular suggestions of the Schrödinger and Dirac equations don't have been continuously rejected: they are often valid and worthwhile for explaining a few experimental effects, e.g., the high-energy tail of the linear momentum distribution within the flooring kingdom of hydrogenic atoms. moment, it's established that cost trade will never be an inherently quantal phenomenon, yet fairly has classical roots. This result's utilized to the matter of continuum decreasing in plasmas. 3rd, it's proven that the main difficult challenge of classical physics that ended in the improvement of quantum mechanics the failure to give an explanation for the soundness of atoms will be truly solved inside a classical formalism from first rules: the autumn of atomic electrons at the nucleus as a result of the radiative lack of the strength, which classically unavoidable, doesn't ensue inside Dirac's generalized Hamiltonian dynamics utilized to atomic physics. The underlying physics might be interpreted as a non-Einsteinian time dilation. Fourth, it's confirmed that during two-electron atoms or ions, the spin spin interplay, which used to be frequently regarded as an unimportant correction to the binding strength, really makes an important contribution to the binding power if the singular nature of this interplay is correctly taken under consideration.

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The dependence of the equilibrium value of the scaled radius v ≡ ρ/R of the electron orbit on the scaled axial coordinate w ≡ z/R of the electron for the ratio of nuclear charges Z /Z = 3. For b < 1, the equilibrium value of v exists for 0 ≤ w < b/(1 + b) and for 1/(1 + b1/2 ) ≤ w ≤ 1. For b > 1, the equilibrium value of v exists for 0 ≤ w ≤ 1/(1 + b1/2 ) and for b/(1 + b) < w ≤ 1. For b = 1, the equilibrium value of v exists for the entire range of 0 ≤ w ≤ 1. Below we refer to these intervals as the “allowed ranges” of w.

84) 3/2 ((1 − w)2 + p) The quantities ε1 and r now depend only on the coordinates w and p (besides the constant λ). Therefore, if we solve Eq. 84) for p and substitute it into Eqs. 83), we obtain the parametric solution for the energy terms ε1 (r) with the parameter w for the given b and λ. 84) does not allow an exact analytical solution for p. Therefore, we will use an approximate analytical method. 1. As in Sec. 5, the plot has two branches, the left one spanning from w = 0 to w = w1 , and the right one from the asymptote w = w3 to w = 1.

Any b. If v0 (w, b) < vcrit (w), the equilibrium is unstable: the quantity ω− takes imaginary values; its absolute value |ω− | is the increment of the instability developing in the direction of the normal coordinate δw . 31) still holds for any b. Thus, for the stable motion, the electron trajectory is a helix on the surface of a cone, with the axis coinciding with the internuclear axis. In this helical state, the electron, while spiraling on the surface of the cone, oscillates between two end-circles which result from cutting the cone by two parallel planes perpendicular to its axis (Fig.