A symmetric matrix method for Schrodinger eigenstates

Dunn, Dennis; Grieves, Brian

doi:10.1088/0305-4470/22/23/003

Cited by 13 publications

(8 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If the point x 0 is the point where E is equal to the potential height, (4) becomes equivalent to Numerov process [2]. As a wave function's amplitude is spatially varied, the slope of probability has various values at x 0 .…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

An effective algorithm for numerical Schrödinger solver of quantum well structures

2008

View full text Add to dashboard Cite

An effective algorithm for a one dimensional Schrödinger solver is proposed. The algorithm is derived from Bohm's form of Schrödinger equation, and can be interpreted as a generalization of the Numerov process for the computational solution to the Schrödinger equation with quantum well structures. The proposed algorithm averages the probability slope's discontinuity to converge the given energy to the nearest eigenstate, and generate complete eigenstates in a general heterojunction potential well. The new algorithm is applied to double-well III-V nanoscale MOSFET and generates each of the quantized levels.

show abstract

Section: Methodsmentioning

confidence: 99%

“…The eigenfunctions of a quantum well can be obtained using a symmetric matrix method [2] or Numerov method [3].…”

Section: Introductionmentioning

confidence: 99%

An effective algorithm for numerical Schrödinger solver of quantum well structures

2008

View full text Add to dashboard Cite

show abstract

“…[26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] When the variational method is applied to the centralforce problem, the functional E͓͔ given in Eq. If for the problem under study there is no known exact solution, one has to approximate it by using a variety of techniques.…”

Section: B Radial Schrödinger Equationmentioning

confidence: 99%

Variational solution of the Schrödinger equation using plane waves in adaptive coordinates: The radial case

Pérez‐Jordá

2010

The Journal of Chemical Physics

View full text Add to dashboard Cite

A new method for solving the Schrödinger equation is proposed, based on the following details. First, a map u=u(r) from Cartesian coordinates r to a new coordinate system u is chosen. Second, the solution (orbital) psi(r) is written in terms of a function U depending on u so that psi(r)=/J(u)/(-1/2)U(u), where /J(u)/ is the Jacobian determinant of the map. Third, U is expressed as a linear combination of plane waves in the u coordinate, U(u)= sum (k)c(k)e(ik x u). Finally, the coefficients c(k) are variationally optimized to obtain the best energy, using a generalization of an algorithm originally developed for the Coulomb potential [J. M. Perez-Jorda, Phys. Rev. B 58, 1230 (1998)]. The method is tested for the radial Schrödinger equation in the hydrogen atom, resulting in micro-Hartree accuracy or better for the energy of ns and np orbitals (with n up to 5) using expansions of moderate length.

show abstract

“…Such spacetimes are characterized by a kink-number k ∈ Z therefore. In subsequent works then it has been shown that all spacetimes with k = 0 have a "twisting light-cone structure" and gravitational kinks were in part viewed as "black holes without curvature singularities" (cf., e.g., [4,5,6]). This connection of homotopical considerations with those concerning the causal structure becomes most transparent for 1+1 dimensional spacetimes, which, as often, may serve as a suitable laboratory to improve one's understanding of the role of kinks in gravitational theories [7].…”

Section: Introductionmentioning

confidence: 99%

“…Each such half-turn of the lightcone clearly defines a non-contractible loop in Ω, which may serve as generator of π 1 (Ω). 1 In the literature 1+1 kink metrics have often been written down in explicit coordinates only [6,7,8]. Their kink nature is then usually shown by studying the behaviour of the lightcone as sketched briefly in the example above.…”

Section: Introductionmentioning

confidence: 99%

Global view of kinks in 1+1 gravity

Klösch¹,

Strobl²

1998

Phys. Rev. D

View full text Add to dashboard Cite

Following Finkelstein and Misner, kinks are nontrivial field configurations of a field theory, and different kink numbers correspond to different disconnected components of the space of allowed field configurations for a given topology of the base manifold. In a theory of gravity, nonvanishing kink numbers are associated with a twisted causal structure. In two dimensions this means, more specifically, that the light cone tilts around ͑nontrivially͒ when going along a noncontractible non-self-intersecting loop on spacetime. One purpose of this paper is to construct the maximal extensions of kink spacetimes using Penrose diagrams. This will yield surprising insights into their geometry but also allow us to give generalizations of some well-known examples such as the bare kink and the Misner torus. However, even for an arbitrary 2D metric with a Killing field we can construct continuous one-parameter families of inequivalent kinks. This result has already interesting implications in the flat or de Sitter case, but it applies, e.g., also to generalized dilaton gravity solutions. Finally, several coordinate systems for these newly obtained kinks are discussed.

show abstract

A symmetric matrix method for Schrodinger eigenstates

Cited by 13 publications

References 5 publications

An effective algorithm for numerical Schrödinger solver of quantum well structures

An effective algorithm for numerical Schrödinger solver of quantum well structures

Variational solution of the Schrödinger equation using plane waves in adaptive coordinates: The radial case

Global view of kinks in 1+1 gravity

Contact Info

Product

Resources

About