Occurrence of CuAl2in Duralumin

Some consequences of the generalized uncertainty principle induced ultraviolet wave-vector cutoff in one-dimensional quantum mechanics

“…Here we give a short summary of some mathematical results [61] relevant for the self-adjoint extension of the coordinate operator (c.f. also [14,[26][27][28][29][30][31][32]). In the wavevector representation the states are represented by the wavevector wavefunctionsψ(k x ), the coordinate operator by the formal differential operator i∂ kx (it is called formal because the definition of an operator should include the boundary conditions set on the functions on which it operates, as well).…”

“…Nevertheless, there should be a distinction of Quantum Mechanics discretized on a grid and the case discussed here. In the latter case space reveals discrete and continuous features at the same time, similarly as information does [26][27][28][29][30][31][32][33][34][35][36]. Namely, the physical content of any of the discrete coordinate representations R θ should be identical, i.e.…”

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and f = exp(α|p x |) with F (u) = (1 − e −|u| ) sign u used after Taylor expansion in [23,24] and all implying K ≈ 1/α and a ≈ α ≈ ℓ P .Coordinate space turns out to exhibit features of discreteness [25] and continuity at the same time like information does [26][27][28][29][30][31][32]. The main idea is that space can be thought of a differentiable manifold, but the physical

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Particle in a cavity in one-dimensional bandlimited quantum mechanics

“…In our previous paper [1] we discussed in detail that such a decomposition of any physical state corresponds to the generalization of Shannon's sampling theorem [34]. In bandlimited quan-tum mechanics the coordinate space turns out to exhibit features of discreteness [35] and continuity at the same time like information does [36][37][38][39][40][41][42]. The main idea is that space can be thought of a differentiable manifold, but the physical degrees of freedom cannot fill it in arbitrarily dense manner.…”