THERMODYNAMIC FORMALISM FOR QUANTUM-MECHANICAL SYSTEMS

Based on the thermodynamic formalism of dynamical systems I present an alternative formulation of Euclidean quantum mechanics on the lattice. A class of deterministic chaotic maps is introduced that simulate nonrelativistic quantum-mechanical systems with arbitrary scalar and vector potential. Applying thermodynamic formalism to these maps the partition function converges to the propagator of the Schrodinger equation (with imaginary time) and the free energy to the ground state energy in an appropriate scaling limit. To illustrate the method I determine ground state energies for the harmonic and anharmonic oscillator, and calculate the integrated propagator of the hydrogen atom.