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We investigate the iterated Kronecker product of a square matrix with itself and prove an invariance property for symmetric subspaces. This motivates the definition of an iterated symmetric Kronecker product and the derivation of an explicit formula for its action on vectors. We apply our result for describing a linear change in the matrix parametrization of semiclassical wave packets.
Let $det_2(A)$ be the block-wise determinant (partial determinant). We consider the condition for completing the determinant $det(det_2(A)) = det(A),$ and characterize the case for an arbitrary Kronecker product $A$ of matrices over an arbitrary fiel
In this paper we compare three different orthogonal systems in $mathrm{L}_2(mathbb{R})$ which can be used in the construction of a spectral method for solving the semi-classically scaled time dependent Schrodinger equation on the real line, specifica
Quantum fields do not satisfy the pointwise energy conditions that are assumed in the original singularity theorems of Penrose and Hawking. Accordingly, semiclassical quantum gravity lies outside their scope. Although a number of singularity theorems
We justify WKB analysis for Hartree equation in space dimension at least three, in a regime which is supercritical as far as semiclassical analysis is concerned. The main technical remark is that the nonlinear Hartree term can be considered as a semi
We present a simple formula for the generating function for the polynomials in the $d$--dimensional semiclassical wave packets. We then use this formula to prove the associated Rodrigues formula.