Position eigenstates , symmetries , and the redundant hermiticity of free - particle
نویسنده
چکیده
The quantum state of a particle can be completely specified by a position at one instant of time. This implies a lack of information, hence a symmetry, as to where the particle will move. We here study the consequences for free particles of spin 0 and spin 1/2. On a cubic spatial lattice a hopping equation is derived, and the continuum limit taken. Spin 0 leads to the Schrödinger equation, and spin 1/2 to the Weyl equation. Both Hamiltonians are hermitian automatically, if time-reversal symmetry is assumed. Hopping amplitudes with a " slight " inhomogeneity lead to the Weyl equation in a metric-affine space-time.
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