INTRINSIC RESONANCE REPRESENTATION OF QUANTUM-MECHANICS

The choice of basis states in quantum calculations can be influenced b y several requirements, and sometimes a very natural basis suggests it self. However often one retreats to a ''merely complete'' basis, whose coefficients in the eigenstates carry Little physical insight. We sug gest here an optimal representation, based purely on classical mechani cs. ''Hidden'' constants of the motion and good actions already known to the classical mechanics are thus incorporated into the basis, leavi ng the quantum effects to be isolated and included by small matrix dia gonalizations. This simplifies the hierarchical structure of couplings between ''zero-order'' states. We present a (non-perturbative) method to obtain such a basis-state as solutions to a certain resonant Hamil ton-Jacobi equation. (C) 1997 American Institute of Physics.