Dipole excitation of Na clusters with a non-local energy density functional

Puente, A.; Serra, Llorenç; Casas, M.

doi:10.1007/bf01445008

Cited by 79 publications

(64 citation statements)

References 19 publications

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“…The bound state spectra of systems with effective mass are relavant in many areas such as the study of nuclei [28] and metal clusters [29]. However, in other fields such as for instance electronic properties of semiconductors, one is interested in the properties of quantum systems with nonconstant mass endowed with continuum spectra [1,10,11].…”

Section: Discussionmentioning

confidence: 99%

Supersymmetric Approach to Exactly Solvable Systems With Position-Dependent Effective Masses

2002

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We discuss the relationship between exact solvability of the Schrödinger equation with a position-dependent mass and the ordering ambiguity in the Hamiltonian operator within the frame of supersymmetric quantum mechanics. The one-dimensional Schrödinger equation, derived from the general form of the effective mass Hamiltonian, is solved exactly for a system with exponentially changing mass in the presence of a potential with similar behaviour, and the corresponding supersymmetric partner Hamiltonians are related to the effective-mass Hamiltonians proposed in the literature.

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Section: Discussionmentioning

confidence: 99%

Supersymmetric Approach to Exactly Solvable Systems With Position-Dependent Effective Masses

2002

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“…The appearance of PDEM is also well known in the energy density functional approach to the nuclear many-body problem [4] and its applications [5,6] in the context of nonlocal terms of the accompanying potential. Other theoretical considerations where PDEM has been exploited include the derivation [7] of the underlying electron Hamiltonian from instantaneous Galilean invariance and implementation of the path integral techniques [8] to calculate the Green's function [9] for step and rectangular-barrier potentials and masses.…”

Section: Introductionmentioning

confidence: 99%

A General Scheme for the Effective-Mass Schrödinger Equation and the Generation of the Associated Potentials

et al. 2004

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A systematic procedure to study one-dimensional Schrödinger equation with a position-dependent effective mass (PDEM) in the kinetic energy operator is explored. The conventional free-particle problem reveals a new and interesting situation in that, in the presence of a mass background, formation of bound states is signalled. We also discuss coordinate-transformed, constant-mass Schrödinger equation, its matching with the PDEM form and the consequent decoupling of the ambiguity parameters. This provides a unified approach to many exact results known in the literature, as well as to a lot of new ones.Running head: Effective-Mass Schrödinger Equation

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“…The PDEM concept has been considered in the energydensity functional approach to the quantum many-body problem in the context of nonlocal terms of the accompanying potential and applied to nuclei [4], quantum liquids [5] and metal clusters [6], for instance. Some other theoretical advances include the derivation of the underlying electron Hamiltonian from instantaneous Galilean invariance [7] and the calculation of Green's function for step and rectangular-barrier potentials and masses [8] by implementing path-integral techniques [9].…”

Section: Introductionmentioning

confidence: 99%

Deformed shape invariance and exactly solvable Hamiltonians with position-dependent effective mass

Bagchi

Banerjee

Quesne

et al. 2005

J. Phys. A: Math. Gen.

201

268

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Known shape-invariant potentials for the constant-mass Schrödinger equation are taken as effective potentials in a position-dependent effective mass (PDEM) one. The corresponding shape-invariance condition turns out to be deformed. Its solvability imposes the form of both the deformed superpotential and the PDEM. A lot of new exactly solvable potentials associated with a PDEM background are generated in this way. A novel and important condition restricting the existence of bound states whenever the PDEM vanishes at an end point of the interval is identified. In some cases, the bound-state spectrum results from a smooth deformation of that of the conventional shape-invariant potential used in the construction. In others, one observes a generation or suppression of bound states, depending on the mass-parameter values. The corresponding wavefunctions are given in terms of some deformed classical orthogonal polynomials.

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Dipole excitation of Na clusters with a non-local energy density functional

Cited by 79 publications

References 19 publications

Supersymmetric Approach to Exactly Solvable Systems With Position-Dependent Effective Masses

Supersymmetric Approach to Exactly Solvable Systems With Position-Dependent Effective Masses

A General Scheme for the Effective-Mass Schrödinger Equation and the Generation of the Associated Potentials

Deformed shape invariance and exactly solvable Hamiltonians with position-dependent effective mass

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