# Physical Applications Related to Differentiable Deformations of Poisson Brackets: Quantum Mechanics

@inproceedings{Flato1980PhysicalAR, title={Physical Applications Related to Differentiable Deformations of Poisson Brackets: Quantum Mechanics}, author={Mosh{\'e} Flato and Daniel Sternheimer}, year={1980} }

- Published 1980
DOI:10.1007/978-94-009-8961-0_12

Quantum mechanics is usually formulated in terms of linear operators on a Hilbert space of physical states, while classical mechanics relies on the algebra N of functions over phase-space. In one of the most naive presentations, it is said that the passage from classical to quantum mechanics is realized through the correspondence principle of Bohr, according to which one replaces the position variable q by the operator of multiplication by q, momentum p by iℏ∂/∂q where ℏ is the Planck constant… CONTINUE READING