Self-adjoint quantization of Stäckel integrable systems

Published 30 Jan 2025 in math.DG, math-ph, and math.MP | (2501.18082v2)

Abstract: We show that quadratic Hamiltonians in involution coming from a St\"ackel system are quantizable, in the sense that one can construct commutative self-adjoint operators whose symbols are the quadratic Hamiltonians. Moreover, they allow multiplicative separation of variables. This proves a conjecture explicitly formulated in [3].

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