Analysis of asymmetric confined quantum systems by the direct variational method

1995 ◽  
Vol 63 (5) ◽  
pp. 460-463 ◽  
Author(s):  
J. L. Marín ◽  
R. Rosas ◽  
A. Uribe
Keyword(s):  
Variational Method ◽  
Quantum Systems ◽  
Direct Variational Method ◽  
Confined Quantum Systems

Ferroelectricity enhancement in confined nanorods: Direct variational method

2006 ◽  
Vol 73 (21) ◽  
Author(s):  
Anna N. Morozovska ◽  
Eugene A. Eliseev ◽  
Maya D. Glinchuk
Keyword(s):  
Variational Method ◽  
Direct Variational Method

scholarly journals Variational and Topological Methods for a Class of Nonlinear Equations which Involves a Duality Mapping

2020 ◽  
pp. 56-71
Author(s):  
Jenica Cringanu
Keyword(s):  
Banach Space ◽  
Variational Method ◽  
Critical Points ◽  
Mountain Pass Theorem ◽  
Growth Conditions ◽  
Existence Results ◽  
Duality Mapping ◽  
Topological Methods ◽  
Carathéodory Function ◽  
Direct Variational Method

The purpose of this paper is to show the existence results for the following abstract equation Jpu = Nfu,where Jp is the duality application on a real reflexive and smooth X Banach space, that corresponds to the gauge function φ(t) = tp-1, 1 < p < ∞. We assume that X is compactly imbedded in Lq(Ω), where Ω is a bounded domain in RN, N ≥ 2, 1 < q < p∗, p∗ is the Sobolev conjugate exponent.Nf : Lq(Ω) → Lq′(Ω), 1/q + 1/q′ = 1, is the Nemytskii operator that Caratheodory function generated by a f : Ω × R → R which satisfies some growth conditions. We use topological methods (via Leray-Schauder degree), critical points methods (the Mountain Pass theorem) and a direct variational method to prove the existence of the solutions for the equation Jpu = Nfu.

Confined quantum systems and their limits

2009 ◽  
Vol 50 (2) ◽  
pp. 022101 ◽  
Author(s):  
Francesco Belgiorno ◽  
Franco Gallone
Keyword(s):  
Quantum Systems ◽  
Confined Quantum Systems

scholarly journals ON AN ELLIPTIC SYSTEM OF P(X)-KIRCHHOFF-TYPE UNDER NEUMANN BOUNDARY CONDITION

2012 ◽  
Vol 17 (2) ◽  
pp. 161-170 ◽  
Author(s):  
Zehra Yucedag ◽  
Mustafa Avci ◽  
Rabil Mashiyev
Keyword(s):  
Boundary Condition ◽  
Weak Solution ◽  
Variational Principle ◽  
Variational Method ◽  
Elliptic System ◽  
Neumann Boundary Condition ◽  
Existence Of Solutions ◽  
Neumann Boundary ◽  
Kirchhoff Type ◽  
Direct Variational Method

In the present paper, by using the direct variational method and the Ekeland variational principle, we study the existence of solutions for an elliptic system of p(x)-Kirchhoff-type under Neumann boundary condition and show the existence of a weak solution.

WKB quantization rules for three-dimensional confinement

2001 ◽  
Vol 79 (6) ◽  
pp. 939-946 ◽  
Author(s):  
A Sinha ◽  
R Roychoudhury ◽  
Y P Varshni
Keyword(s):  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Reasonable Agreement ◽  
Three Dimensional ◽  
Quantum Systems ◽  
The Past ◽  
Two Systems ◽  
Mathematical Techniques ◽  
Confined Quantum Systems ◽  
Quantization Rules

Confined quantum systems have been studied by various authors over the past decades, by using various mathematical techniques. In this work, we derive the WKB quantization rules for quantum systems confined in an impenetrable spherical box of radius r0. We apply the proposed method to two systems explicitly, viz., the confined harmonic oscillator and the confined hydrogen atom. The results are found to be in reasonable agreement with those obtained by other methods. PACS No.: 03.65

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