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arXiv · hep-th/9712052

Constrained Dynamics for Quantum Mechanics I. Restricting a Particle to a Surface

Hendrik Grundling·C. A. Hurst
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Abstract

We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of constraining and dynamics adjustment which produces the right Hamiltonian on the submanifold when tested on known examples. This method we hope will become the germ of a full Dirac algorithm for quantum constraints. We take a first step in generalising it to the situation where the constraint is a general selfadjoint operator with some additional structures.

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Hendrik Grundling, C. A. Hurst. 1997-12-05. Constrained Dynamics for Quantum Mechanics I. Restricting a Particle to a Surface. https://doi.org/10.1063/1.532241

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