Abstract
In this chapter we give a concise review of the quantum mechanics formalism from a perspective which generalizes the ordinary Schroedinger formulation. In this way we may reconsider the Schroedinger approach to quantum mechanics from a more geometrical and group-theoretical point of view and show the close relationship between the classical Hamiltonian theory and quantum mechanics. Moreover the formalism developed in this chapter will be useful for an appropriate exposition of the relativistic wave equations in Chap. 10 and the field quantization approach in Chap. 11.
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