Self-adjoint quantization of Stäckel integrable systems

Abstract We show that quadratic Hamiltonians in involution coming from a Stäckel 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 Błaszak et al (2016 Ann. Phys., NY 371 460–77).