Self-adjoint quantization of Stäckel integrable systems

J. M. Kress; Vladimir S. Matveev

doi:10.1088/1751-8121/adf786

August 4, 2025Journal of Physics A Mathematical and TheoreticalOpen Access

Self-adjoint quantization of Stäckel integrable systems

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Key Points

Quadratic Hamiltonians from Stäckel systems can be quantized into self-adjoint operators, enabling new methodologies.
This study demonstrates that the self-adjoint operators have symbols matching the quadratic Hamiltonians, affirming established conjectures.
Commutative self-adjoint operators support multiplicative separation of variables, which is crucial for integrability.
The findings highlight the potential mathematical advancements in quantization within integrable systems, calling for further explorations.

Implication

Analysis shows quantization of quadratic Hamiltonians in Stäckel systems, indicating multiplicative separation of variables.

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 [3].

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Cite This Study

Kress et al. (2025) studied this question.

synapsesocial.com/papers/68c1b18b54b1d3bfb60e88ca https://doi.org/10.1088/1751-8121/adf786

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Self-adjoint quantization of Stäckel integrable systems

Key Points

Implication

Abstract

Discussion

Cite This Study

Self-adjoint quantization of Stäckel integrable systems

Key Points

Implication

Abstract

Discussion

Cite This Study

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