A particle in a box in the presence of an electric field and applications to disordered systems

Lukes, Timothy J.; Ringwood, Graem A.; Suprapto, B.

doi:10.1016/0378-4371(76)90011-x

Cited by 25 publications

(16 citation statements)

References 2 publications

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“…As conclusion let us also mention that in the limit of L=R 1 → 0 the results of this paper in natural way agrees the results for electrical absorption in case of "ordinary" plane-parallel quantized ÿlm [9,10].…”

Section: Discussion Of Resultssupporting

confidence: 86%

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Confinement Stark effect and electroabsorption in semiconductor cylindrical layer

Harutyunyan

Aramyan

Petrosyan

2004

Physica E: Low-dimensional Systems and Nanostructures

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Section: Discussion Of Resultssupporting

confidence: 86%

“…(6) into Eq. (9) and using (0) (R 1 ) = (0) (R 2 ) = 0 (10) boundary conditions, one can correspondingly obtain for the total energy of particle transversal motion E n; m and radial envelop wave functions…”

Section: Electronical States In the Layermentioning

confidence: 99%

Confinement Stark effect and electroabsorption in semiconductor cylindrical layer

Harutyunyan

Aramyan

Petrosyan

2004

Physica E: Low-dimensional Systems and Nanostructures

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“…(45) are easily calculated on the basis of the method proposed in Ref. for the Dirichlet case. As an example, let us consider its application for the ground state,

n = 0

, of the Zaremba geometry.…”

Section: Resultsmentioning

confidence: 99%

“…For reference, the expressions for the three lowest levels at

E ≪ 1

are provided below:

\begin{matrix} true \\ right E_{0}^{D D} (E) = 1 - \frac{1}{48} (() \frac{15}{π^{2}} - 1) E^{2} = 1 - 0.0108 E^{2} \end{matrix}

\begin{matrix} true \\ right E_{1}^{D D} (E) = 4 + ((), \frac{1}{192} - \frac{5}{256} \frac{1}{π^{2}}) E^{2} = 4 + 0.00323 E^{2} \end{matrix}

\begin{matrix} true \\ right E_{2}^{D D} (E) = 9 + \frac{1}{2^{4} \cdot 3^{3}} (() 1 - \frac{5}{3} \frac{1}{π^{2}}) E^{2} = 9 + 0.00192 E^{2} \end{matrix}

(Eq. was derived before either with the help of the perturbation calculations or variational approach or hypervirial‐perturbational treatment )

\begin{matrix} true \\ right E_{0}^{N D} (E) & = & left \frac{1}{4} + \frac{2}{π^{2}} scriptE + (() \frac{1}{12} + \frac{1}{π^{2}} - \frac{20}{π^{4}}) E^{2} \\ = & left 0.25 + 0.203 scriptE - 0.0207 E^{2} \end{matrix}

…”

Section: Resultsmentioning

confidence: 99%

Comparative analysis of electric field influence on the quantum wells with different boundary conditions.

Olendski

2015

Annalen der Physik

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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 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 , 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 are BC independent and for all states but the ground Neumann level (which has ) are equal to while the momentum entropies 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.

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“…o El estudio de los electrones de Bloch en un campo eléctrico y el efecto Stark o El estudio de la densidad de estados de un sistema desordenado en presencia de un campo eléctrico [69].…”

Section: Introdución 1 Importancia De Los Sistemas Cuánticos Confinadosunclassified

Uso del método de series para el estudio de sistemas cuánticos confinados

Aquino

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Importancia de los sistemas cuánticos confinados. 1 2 Objetivo de este trabajo. 3 3 Contenido del trabajo. 4 l. Metodología en el estudio de los Sistemas Cuánticos Confinados l. 1 Métodos comunmente empleados. 7 l. l. 1 Métodos exactos. 7 l. 1.2 Método variacional directo. 10 l. 1.3 Métodos perturbativos. 1 1 l. 1.4 Método de perturbación de fronteras. 12 l . 1.5 Teorema del Virial. 14 l. 1.6 Otros métodos. 16 1.2 Método de series. 17 2. El oscilador armónico isotrópico confinado. 2.1 Antecedentes. 21 2.2 Eigenvalores de la energía. 22 2.3 Los valores esperados de la posición. 30 2.4 Conclusiones. 33 3. Atorno de hidrógeno 3D confinado. 3.1 Antecedentes. 3 5 3.2 El confinamiento dentro de cajas impenetrables. 36

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A particle in a box in the presence of an electric field and applications to disordered systems

Cited by 25 publications

References 2 publications

Confinement Stark effect and electroabsorption in semiconductor cylindrical layer

Confinement Stark effect and electroabsorption in semiconductor cylindrical layer

Comparative analysis of electric field influence on the quantum wells with different boundary conditions.

Uso del método de series para el estudio de sistemas cuánticos confinados

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