Hilbert space representation of the minimal length uncertainty relation.
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Cites background or methods from "Hilbert space representation of the..."
...[323, 322], which is centered on a modification of the Heisenberg principle...
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...Especially this second point is rather significant since heuristic arguments of the type also used to motivate modified dispersion relations suggest [22, 122, 323, 415, 243, 408] that the Heisenberg commutator might have to be modified in the quantum-spacetime realm....
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Cites background from "Hilbert space representation of the..."
...To that end, one changes the measure in momentum space to [175, 184]...
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...It has been shown in [184] that the sharply-peaked wavefunctions with spread below the minimal position uncertainty carry an infinite energy, and thus do not represent a physically-meaningful basis....
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...[175, 174, 184, 178] developed the mathematical basis of quantum mechanics that took into account a minimal length scale and ventured towards quantum field theory....
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...In [184], the maximal localization states have been constructed in one spatial dimension for a 2nd-order expansion of the GUP....
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...In this fashion, in the leading-order approximation, the harmonic oscillator in one dimension has been studied in [184, 167, 8, 125], the harmonic oscillator in arbitrary dimensions in [83, 177, 85, 93], the energy levels of the hydrogen atom in [167, 69, 296, 67, 258], the particle in a box in [7], Landau levels and the tunneling current in [8, 96, 97], the uniform gravitational potential in [244, 83], the inverse square potential in [65, 66], neutrino oscillations in [292], reflection and transmission coefficients of a potential step and potential barrier in [8, 97], the Klein paradox in [124], and corrections to the gyromagnetic moment of the muon in [143, 95]....
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