Quantum mechanics on a real Hilbert space

Details Quantum mechanics on a real Hilbert space Quantum mechanics on a real Hilbert space

1999-05-11

arxiv.org/abs/quant-ph/9905037v1

Physics

Quantum Physics

13 pages, LaTeX, no figures

Scientific paper

The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics, keeping the same set of physical states, but admitting more general observables. The standard time reversal operator involves complex conjugation, in this sense it goes beyond the complex theory and may serve as an example to motivate the generalization. Another example is unconventional canonical quantization such that the harmonic oscillator of angular frequency $\omega$ has any given finite or infinite set of discrete energy eigenvalues, limited below by $\hbar\omega/2$.

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