Abstract
Abstract We begin the discussion of nonrelativistic quaternionic quantum mechanics by analyzing the allowed form of H for a single-particle system. We will assume, as is done in complex nonrelativistic quantum mechanics, that H is invariant under Galilean transformations and that the kinetic or noninteracting part of H is rotation and translation invariant. In analyzing the implications of these assumptions, we follow the method used in Sec. 13-4 of Jauch (1968a) in the complex quantum mechanics case [see also Mackey (1968), and Feynman as described in Dyson (1990)], and so work in the coordinate representation (cf. Sec. 2.4), and use the Heisenberg picture (cf. Sec. 3.3) to describe time evolution. For brevity of notation, we omit the subscript H for Heisenberg picture operators and denote the coordinate representation Hamiltonian H(x) as simply H2.
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