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Comparative analysis of electric field influence on the quantum wells with different boundary conditions. I. Energy spectrum, quantum information entropy and polarization | | O. Olendski
; | | Date: |
10 Feb 2015 | | Abstract: | Analytical solutions of the Schr"{o}dinger equation for the one-dimensional
quantum well with all possible permutations of the Dirichlet and Neumann
boundary conditions (BCs) in perpendicular to the interfaces uniform electric
field $mathscr{E}$ are used for the comparative investigation of their
interaction and its influence on the properties of the system. Limiting cases
of the weak and strong voltages allow an easy mathematical treatment and its
clear physical explanation; in particular, for the small $mathscr{E}$, the
perturbation theory derives for all geometries a linear dependence of the
polarization on the field with the BC-dependent proportionality coefficient
being positive (negative) for the ground (excited) states. Simple two-level
approximation elementary explains the negative polarizations as a result of the
field-induced destructive interference of the unperturbed modes and shows that
in this case the admixture of only the neighboring states plays a dominant
role. Different magnitudes of the polarization for different BCs in this regime
are explained physically and confirmed numerically. Hellmann-Feynman theorem
reveals a fundamental relation between the polarization and the speed of the
energy change with the field. It is proved that zero-voltage position entropies
$S_x$ are BC independent and for all states but the ground Neumann level (which
has $S_x=0$) are equal to $ln2-1$ while the momentum entropies $S_k$ depend on
the edge requirements and the level. Varying electric field changes position
and momentum entropies in the opposite directions such that the entropic
uncertainty relation is satisfied. | | Source: | arXiv, 1502.3013 | | Services: | Forum | Review | PDF | Favorites | |
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