For many physicists who live on intimate terms with atoms, molecules, solids or particles, classical mechanics is a necessary evil, sometimes needed to provide a Hamiltonian or Lagrangian, and hastily abandoned when it has served this purpose. It was not always so: those who worked with Niels Bohr and Max Born in the early 1920s had no quantum mechanics to turn to: they had to do their best with classical mechanics and the old quantum theory.
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I C Percival (1980) studied this question.