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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.

Olendski O - Ann Phys (2015)

Bottom Line: 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.Applications to different branches of physics, such as ocean fluid dynamics and atmospheric and metallic waveguide electrodynamics, are discussed.

View Article: PubMed Central - PubMed

Affiliation: King Abdullah Institute for Nanotechnology, King Saud University P.O. Box 2455, Riyadh, 11451, Saudi Arabia.

ABSTRACT

Analytical solutions of the Schrödinger 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 [Formula: see text] 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 [Formula: see text], 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 [Formula: see text] are BC independent and for all states but the ground Neumann level (which has [Formula: see text]) are equal to [Formula: see text] while the momentum entropies [Formula: see text] 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. Other physical quantities such as the BC-dependent zero-energy and zero-polarization fields are also studied both numerically and analytically. Applications to different branches of physics, such as ocean fluid dynamics and atmospheric and metallic waveguide electrodynamics, are discussed.

No MeSH data available.


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The same as in Fig.5 but for the ground state function . For the DN geometry, the viewing location is different as compared to other BCs.
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fig06: The same as in Fig.5 but for the ground state function . For the DN geometry, the viewing location is different as compared to other BCs.

Mentions: Comparison of Eqs. (60) and (61) proves that for the ground level the dominant admixture comes from the nearest lying excited state while the contributions from the higher levels can be safely neglected. Eq. (59) tells us that for the lowest level the application of the field leads to such deformation of the particle concentration inside the well that is consistent with the rules of the classical mechanics: probability of finding the electron at the right (left) wall increases (decreases) with the electric force. Dependence on the field of the ground state wavefunctions for all possible I and J is shown in Fig.6.


Comparative analysis of electric field influence on the quantum wells with different boundary conditions.: I. Energy spectrum, quantum information entropy and polarization.

Olendski O - Ann Phys (2015)

The same as in Fig.5 but for the ground state function . For the DN geometry, the viewing location is different as compared to other BCs.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4402006&req=5

fig06: The same as in Fig.5 but for the ground state function . For the DN geometry, the viewing location is different as compared to other BCs.
Mentions: Comparison of Eqs. (60) and (61) proves that for the ground level the dominant admixture comes from the nearest lying excited state while the contributions from the higher levels can be safely neglected. Eq. (59) tells us that for the lowest level the application of the field leads to such deformation of the particle concentration inside the well that is consistent with the rules of the classical mechanics: probability of finding the electron at the right (left) wall increases (decreases) with the electric force. Dependence on the field of the ground state wavefunctions for all possible I and J is shown in Fig.6.

Bottom Line: 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.Applications to different branches of physics, such as ocean fluid dynamics and atmospheric and metallic waveguide electrodynamics, are discussed.

View Article: PubMed Central - PubMed

Affiliation: King Abdullah Institute for Nanotechnology, King Saud University P.O. Box 2455, Riyadh, 11451, Saudi Arabia.

ABSTRACT

Analytical solutions of the Schrödinger 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 [Formula: see text] 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 [Formula: see text], 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 [Formula: see text] are BC independent and for all states but the ground Neumann level (which has [Formula: see text]) are equal to [Formula: see text] while the momentum entropies [Formula: see text] 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. Other physical quantities such as the BC-dependent zero-energy and zero-polarization fields are also studied both numerically and analytically. Applications to different branches of physics, such as ocean fluid dynamics and atmospheric and metallic waveguide electrodynamics, are discussed.

No MeSH data available.


Related in: MedlinePlus