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  1.  2
    A Non-relativistic Approach to Relativistic Quantum Mechanics: The Case of the Harmonic Oscillator.Luis A. Poveda, Luis Grave de Peralta, Jacob Pittman & Bill Poirier - 2022 - Foundations of Physics 52 (1):1-20.
    A recently proposed approach to relativistic quantum mechanics is applied to the problem of a particle in a quadratic potential. The methods, both exact and approximate, allow one to obtain eigenstate energy levels and wavefunctions, using conventional numerical eigensolvers applied to Schrödinger-like equations. Results are obtained over a nine-order-of-magnitude variation of system parameters, ranging from the non-relativistic to the ultrarelativistic limits. Various trends are analyzed and discussed—some of which might have been easily predicted, others which may be a bit more (...)
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    Algebraically Self-Consistent Quasiclassical Approximation on Phase Space.Bill Poirier - 2000 - Foundations of Physics 30 (8):1191-1226.
    The Wigner–Weyl mapping of quantum operators to classical phase space functions preserves the algebra, when operator multiplication is mapped to the binary “*” operation. However, this isomorphism is destroyed under the quasiclassical substitution of * with conventional multiplication; consequently, an approximate mapping is required if algebraic relations are to be preserved. Such a mapping is uniquely determined by the fundamental relations of quantum mechanics, as is shown in this paper. The resultant quasiclassical approximation leads to an algebraic derivation of Thomas–Fermi (...)
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  3.  39
    Phase Space Optimization of Quantum Representations: Non-Cartesian Coordinate Spaces. [REVIEW]Bill Poirier - 2001 - Foundations of Physics 31 (11):1581-1610.
    In an earlier article [Found. Phys. 30, 1191 (2000)], a quasiclassical phase space approximation for quantum projection operators was presented, whose accuracy increases in the limit of large basis size (projection subspace dimensionality). In a second paper [J. Chem. Phys. 111, 4869 (1999)], this approximation was used to generate a nearly optimal direct-product basis for representing an arbitrary (Cartesian) quantum Hamiltonian, within a given energy range of interest. From a few reduced-dimensional integrals, the method determines the optimal 1D marginal Hamiltonians, (...)
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