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Algebraic approach to non-separable two-dimensional Schrödinger equation: Ground states for polynomial and Morse-like potentials

100%
Tichý V., Skála L., Hudec R.
Open Physics
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2014
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vol. 12
|
issue 10
730-736
EN
This paper presents a direct algebraic method of searching for analytic solutions of the two-dimensional time-independent Schrödinger equation that is impossible to separate into two one-dimensional ones. As examples, two-dimensional polynomial and Morse-like potentials are discussed. Analytic formulas for the ground state wave functions and the corresponding energies are presented. These results cannot be obtained by another known method.
2
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Quantum cards and quantum rods

100%
Batista M., Peternelj J.
Open Physics
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2008
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vol. 6
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issue 1
171-177
EN
Quantum mechanical analysis of a rigid rod with one end fixed to a flat table is presented. Assuming that the rod is initally in the upright orientation, “the time of fall” is calculated using WKB wavefunctions representing energy eigenstates near the barrier summit.
3
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On the origin of space

100%
Herrmann R.
Open Physics
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2013
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vol. 11
|
issue 10
1212-1220
EN
Within the framework of fractional calculus with variable order the evolution of space in the adiabatic limit is investigated. Based on the Caputo definition of a fractional derivative using the fractional quantum harmonic oscillator a model is presented, which describes space generation as a dynamic process, where the dimension d of space evolves smoothly with time in the range 0 ≤ d(t) ≤ 3, where the lower and upper boundaries of dimension are derived from first principles. It is demonstrated, that a minimum threshold for the space dimension is necessary to establish an interaction with external probe particles. A possible application in cosmology is suggested.
4
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Computational Tools Applied to Enzyme Design − a review

100%
García-Guevara F., Avelar M., Ayala M., Segovia L.
Biocatalysis
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2014
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vol. 1
|
issue 1
EN
The protein design toolbox has been greatly improved by the addition of enzyme computational simulations. Not only do they warrant a more ambitious and thorough exploration of sequence space, but a much higher number of variants and protein-ligand systems can be analyzed in silico compared to experimental engineering methods. Modern computational tools are being used to redesign and also for de novo generation of enzymes. These approaches are contingent on a deep understanding of the reaction mechanism and the enzyme’s three-dimensional structure coordinates, but the wealth of information produced by these analyses leads to greatly improved or even totally new types of catalysis.
5
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Dynamical and structural symmetries for the highest Landau levels on the AdS 2

100%
Espoukeh P., Fakhri H.
Open Physics
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2012
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vol. 10
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issue 2
405-413
EN
The aim of the paper is to use the recurrence relations with respect to both indices of the associated Legendre functions for the extraction of the Dirac quantization condition and dynamical symmetry group U(1, 1) corresponding to the highest Landau levels on the hyperbolic plane with uniform magnetic field B. Irreducible representations of the su(2) algebra are obtained by the ladder differential operators which change B by 1/2 unit and mode number by one unit. Two different classes of the irreducible representations of SU(1, 1) with the even and odd boson numbers 2B − 1/2 are extracted for the Bargmann indices 1/4 and 3/4, respectively. Finally, we show that shape invariance symmetry is realized by the ladder operators which shift only the magnetic field B by 1/2 unit.
6
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Tunnelling time of a gaussian wave packet through two potential barriers

75%
Petrillo V., Olkhovsky V.
Open Physics
|
2005
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vol. 3
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issue 3
339-350
EN
The resonant and non-resonant dynamies of a Gaussian quantum wave packet travelling through a double barrier system is studied as a function of the initial characteristics of the spectrum and of the parameters of the potential. The behaviour of the tunnelling time shows that there are situations where the Hartman effect occurs, while, when the resonances are dominant, and in particular for b>π/Δk (b being the inter-barrier distance and Δk the spectrum width), the tunnelling time becomes very large and the Hartman effect does not take place.
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