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

Puente, A.; Serra, Ll.; Casas, M.

doi:10.1007/978-3-642-79696-8_67

Cited by 3 publications

(7 citation statements)

References 15 publications

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“…for pseudotensor integrals of motion, and µ ab = νµ ab 6 + λµ ab 8 (25) for tensor integrals of motion, were ν, λ and ω are arbitrary parameters. The linear combinations of arbitrary functions appearing in (23) and (24) should be treated as new arbitrary functions.…”

Section: Discussion Of the Determining Equationsmentioning

confidence: 99%

“…Let us remind that just the PDM systems are intensively used in modern physics. They are applied for modeling of condensed-matter systems, namely, semiconductors [20], [21], quantum liquids [22] and metal clusters [23], quantum wells, wires and dots [24], [25] and many, many others. In addition, thanks to the additional randomness connected with a non-fixed mass, the PDM systems present a much more reach field for application of symmetry methods than the systems with constant masses.…”

Section: Introductionmentioning

confidence: 99%

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Superintegrable and shape invariant systems with position dependent mass

Nikitin¹

2015

J. Phys. A: Math. Theor.

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Second order integrals of motion for 3d quantum mechanical systems with position dependent masses (PDM) are classified. Namely, all PDM systems are specified which, in addition to their rotation invariance, admit at least one second order integral of motion. All such systems appear to be also shape invariant and exactly solvable. Moreover, some of them possess the property of double shape invariance and can be solved using two different superpotentials. Among them there are systems with double shape invariance which present nice bridges between the Coulomb and isotropic oscillator systems.A simple algorithm for calculation the discrete spectrum and the corresponding state vectors for the considered PDM systems is presented and applied to solve five of the found systems.

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Section: Discussion Of the Determining Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Superintegrable and shape invariant systems with position dependent mass

Nikitin¹

2015

J. Phys. A: Math. Theor.

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“…where f is the function presented in (28). This linear inhomogeneous equation is solved by the following function:…”

Section: Solution Of Determining Equationsmentioning

confidence: 99%

“…Let us specify these functions by requiring that the corresponding Hamiltonians admit the additional integral of motion M 21 . In this case functions (28) and (30) have to satisfy the following additional equations: (12), (13) and line 7 of Table 1. In other words, functions (28) and (30) have to be independent on their first argument x 2 x 1 .…”

Section: Solution Of Determining Equationsmentioning

confidence: 99%

“…In the present paper we discuss superintegrability aspects of position dependent mass (PDM) Schrödinger equations which attract interest of many researchers and are applied in several physical systems. They are requested for description of various condensedmatter systems such as semiconductors [25], [26], quantum liquids [27] and metal clusters [28], quantum wells, wires and dots [29], [30], supper-lattice band structures [31] and many, many others.…”

Section: Introductionmentioning

confidence: 99%

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Superintegrable systems with position dependent mass

Nikitin

Zasadko

2015

Journal of Mathematical Physics

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First order integrals of motion for Schr\"odinger equations with position dependent masses are classified. Seventeen classes of such equations with non-equivalent symmetries are specified. They include integrable, superintegrable and maximally superintegrable systems. Among them is a system invariant with respect to the Lie algebra of Lorentz group and a system whose integrals of motion form algebra so(4). Three of the obtained systems are solved exactly.Comment: Two unnecessary items are deleted from Table

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The Ordering Ambiguity and Position Dependent Mass for Non- Relativistic Quantum Particle With Inter-Dimensional (D=1)

Alaakol.¹

2016

IJAR

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By revisiting free particle v(x)=0 endowed with position dependent mass = 1 (1+ 2 ) 2 has d=1 (the inter-dimensional). Starting with the kinetic energy operator, we will try to solve the equation by simplification mathematical method to find energy spectrum, then get stander form for the energy whose dependent on the ordering ambiguity. Copy Right, IJAR, 2016,. All rights reserved. …………………………………………………………………………………………………….... Introduction:-Position dependent mass quantum particles in non-relativistic quantum theory have inspired researchers in the last few years [1-4]. They found new useful and interesting models help them in physical obstructions [5], semiconductors [6], quantum dot [7], quantum liquids [8], He-clusters [9] and metal clusters [10].Quantum mechanical particle endowed with PDM erupt in the system of quantum mechanics to solve more problems of a delicate nature like example: the m(x), kinetic energy and the momentum operator does not commute [11].In other side, they try to find a solution for the Schrödinger equation in d-dimensional by dependent a canonical transformation (PCT) method [12,13 ] under task change variables [14][15][16]. The eigenvalues and eigenfunctions are mapped for the exact solutions for Schrödinger equation [17][18][19].Recently, PCT for PDM-quantum particle introduced in d-dimensional [1]. The inter-one degeneracies associated with the isomorphism between angular momentum and dimensionality builds up the ladder of excited states for any given values e.g. nonzero and the radial quantum number . By choosing the parameters = = −1with the PCT method, it lead to get the Schrödinger equation with the effective potential( Poschl-Teller potential) [20].Here, we choose a free particle with = 0, the interdimensional = 1 and keeping on the von-Roos ordering in the general form + + = −1 , we will try to find a new formula for energy spectrum depend on position dependent mass parameters. Time -independent Schrödinger equation in one-dimensional by PCT method:-The stander form time-independent Schrödinger equation is given: − ℏ 2 2 2 2 + = (1)

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

Cited by 3 publications

References 15 publications

Superintegrable and shape invariant systems with position dependent mass

Superintegrable and shape invariant systems with position dependent mass

Superintegrable systems with position dependent mass

The Ordering Ambiguity and Position Dependent Mass for Non- Relativistic Quantum Particle With Inter-Dimensional (D=1)

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