We establish a hierarchy of weighted majorization relations for the singularities of generalized Lamé equations and the zeros of their Van Vleck and Heine-Stieltjes polynomials as well as for multiparameter spectral polynomials of higher Lamé operators. These relations translate into natural dilation and subordination properties in the Choquet order for certain probability measures associated w...

We study the quantum propagator in the semiclassical limit with sharp confining potentials. Including the energy-dependent scattering phase due to sharp confining potential, the modified Van Vleck formula is derived. We also discuss the close relations among quantum statistics, discrete gauge symmetry, and hard-wall constraints. Most of all, we formulate a quantization rule that applies to both...

1 I. Waller, Zeit. Physik, 38, 644 (1926). 2 J. H. Van Vleck, Proc. Roy. Soc. A, 143, 679 (1934). There is a slight error in his expression for r for 1=2, the coefficients being all 10 times too large. 3a may be equated to zero except in the case q = 21. 4 W. N. Bailey, Generalized Hypergeometric Series (Cambridge Tract No. 32), p. 18. 6 The polynomial 1n(Z) is discussed by H. Bateman, T8kohu M...

This is the second installment of a two-part paper on developments in quantum dispersion theory leading up to Heisenberg’s Umdeutung paper. In telling this story, we have taken a paper by John H. Van Vleck (1924b,c) as our main guide. In this second part we present the detailed derivations on which our narrative in the first part rests. The central result that we shall derive is the Kramers dis...

A survey of ligand eld theory is given and the possibility of ob serving the Jahn Teller e ect in molecules by means of gas phase elec tron di raction is discussed The theory of the dynamic Jahn Teller e ect is outlined and theoretical and experimental results for VCl are reviewed In H A Jahn and E Teller predicted that a nonlinear molecule which is in a degenerate state will seek to change its...

Abstract In this paper we consider a spatial discretization scheme with an adaptive grid for the Nagumo PDE. particular, commonly used time dependent moving mesh method that aims to equidistribute arclength of solution under consideration. We assume discrete analogue equidistribution is strictly enforced, which allows us reduce effective dynamics scalar non-local problem infinite range interact...

Abstract In this paper we consider an adaptive spatial discretization scheme for the Nagumo PDE. The is a commonly used mesh adaptation method based on equidistributing arclength of solution under consideration. We assume that equidistribution strictly enforced, which leads to non-local problem with infinite range interactions derived in Hupkes and Van Vleck (J Dyn Differ Equ 28:955, 2016). For...