Self-adjoint realization of the harmonic oscillator in polar coordinates and some consequences
Abstract
We consider spectral decomposition of the harmonic oscillator in Rn in terms of two different orthonormal bases in L2( Rn) consisting of its eigenfunctions. Then, using purely functional analysis tools we provide simple proofs of rotational symmetry of the Hermite projection operators studied by Kochneff, and Thangavelu's Hecke-Bochner type identity.
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