New variational principles in classical and semiclassical mechanics

We demonstrate that reciprocal Maupertuis’ Principle is the classical limit of Schrödinger’s Variational Principle in Quantum Mechanics. Misha Marinov loved analytical mechanics and understood its beauty. Canonical transformations, Poisson structures, symplectic geometry etc. were the notions that he constantly used in his original papers, and in his famous review on path integral. One of the authors (NV) had the pleasure to attend his remarkable lectures at ITEP that preceded the review paper. The subtle relation between Quantum and Classical Mechanics was one of the major subjects in these lectures. We believe that Misha would have enjoyed to read that there exists a new formulation of Classical Mechanics (new variational principle) that follows from Quasiclassical limit of Quantum Mechanics. This paper is based on the results we published in reference [1], and reference [2] in collaboration with Chris Gray. 1 Schrödinger’s Quantum Variational Principle and its Classical Limit. The fundamental theory is Quantum Mechanics. Classical Mechanics is only a special limit of Quantum Mechanics. In other words Quantum mechanics can be a starting point for the derivation of Classical mechanics. One expects