Toeplitz operators and quantum mechanics

Toeplitz operators on the Segal-Bargmann spaces of Gaussian measure square-integrable entire functions on complex n-space Cⁿ are studied. The C^*-algebra generated by the Weyl form of the canonical commutation relations consists precisely of the uniform limits of almost-periodic Toeplitz operators. The question of "which Toeplitz operators admit a symbol calculus modulo the compact operators" is raised and sufficient conditions are given for such a calculus. These conditions involve a notion of "slow oscillation at infinity.".