dorsal/arxiv
View SchemaQuantum mechanics on a real Hilbert space
| Authors | Jan Myrheim |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9905037 |
| URL | https://arxiv.org/abs/quant-ph/9905037 |
Abstract
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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"abstract": "The complex Hilbert space of standard quantum mechanics may be treated as a\nreal Hilbert space. The pure states of the complex theory become mixed states\nin the real formulation. It is then possible to generalize standard quantum\nmechanics, keeping the same set of physical states, but admitting more general\nobservables. The standard time reversal operator involves complex conjugation,\nin this sense it goes beyond the complex theory and may serve as an example to\nmotivate the generalization. Another example is unconventional canonical\nquantization such that the harmonic oscillator of angular frequency $\\omega$\nhas any given finite or infinite set of discrete energy eigenvalues, limited\nbelow by $\\hbar\\omega/2$.",
"arxiv_id": "quant-ph/9905037",
"authors": [
"Jan Myrheim"
],
"categories": [
"quant-ph",
"hep-th"
],
"title": "Quantum mechanics on a real Hilbert space",
"url": "https://arxiv.org/abs/quant-ph/9905037"
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