Spin Eigenfunctions

Pauncz, Ruben

doi:10.1007/978-1-4684-8526-4

Cited by 405 publications

(120 citation statements)

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“…The calculations are performed for each spin multiplicity separately using spin-adapted basis functions. 30 In terms of the matrix elements of the creation and annihilation operators the spectral moments are expressed as…”

Section: Numerical Resultsmentioning

confidence: 99%

Initial stage of quasiparticle decay in fermionic systems

2013

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Generally, the addition or removal of a single particle in a many-body system does not correspond to an exact eigenstate of the system. Thus the resulting coherent excitation evolves in time. As discussed here, the evolution at short times upon the excitation with the energy exhibits a quadratic decay [with the rate constant σ 2 ( )]. Later on, after some time τ ( ), the exponential decay sets in. It is governed by another rate constant γ ( ). This behavior is generic for many realistic finite and extended systems. For a finite system it is possible to assess this behavior full numerically using an exact solution of the many-body problem. We present a simple model for the electron spectral function that links together all three aforementioned parameters and give a prescription for how the energy uncertainty σ 2 ( ) can be computed within the many-body perturbation theory. Our numerical results demonstrate that the model approach accurately reproduces the exact spectral function in a large range of energies even in the case of fragmented many-body states. We show that the central quantity of this study σ 2 ( ) can easily be computed exactly or from approximate theories and, hence, can be used for their validation. We also point out how the set in time can be tested by means of attosecond spectroscopy.

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Section: Numerical Resultsmentioning

confidence: 99%

Initial stage of quasiparticle decay in fermionic systems

2013

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“…If we insert the solution (51) for Φ we obtain a lengthy expression Table 4: Irreducible representation matrices U(P) for N=3. For class and cyclic permutation symbols see [19].…”

Section: Summary and Discussionmentioning

confidence: 99%

Special analytical solutions of the Schrödinger equation for two and three electrons in a magnetic field and ad hoc generalizations toNparticles

Taut

2000

J. Phys.: Condens. Matter

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We found that the two-dimensional Schrödinger equation for 3 electrons in an homogeneous magnetic field (perpendicular to the plane) and a parabolic scalar confinement potential (frequency ω 0 ) has exact analytical solutions in the limit, where the expectation value of the center of mass vector R is small compared with the average distance between the electrons. These analytical solutions exist only for certain discrete values of the effective frequencyω = ω 2 o + ( ωc 2 ) 2 . Further, for finite external fields, the total angular momenta must be M L = 3m with m = integer, and spins have to be parallel. The analytically solvable states are always cusp states, and take the components of higher Landau levels into account. These special analytical solutions for 3 particles and the exact solutions for 2 particles [13] can be written in an unified form. The first set of solutions readswhere p n,m (x) are certain finite polynomials andω n,m is the spectrum 1 of the fields. The pair angular momentum m has to be an odd integer and the integer n defines the number of terms in the polynomials. For infinite solvable fieldsω 1 there is a second set of the formwhere A a is the antisymmetrizer and the pair angular momenta m ik can all be different integers. In both cases the first factor is a shorthand with the convention r m = r |m| e imα . These formulae, when ad hoc generalized to N coordinates, can be discussed as an ansatz for the wave function of the N-particle system. This ansatz fulfills the following demands: it is exact for two particles and for 3 particles in the limit of small R and for the solvable external fields, and it is an eigenfuncton of the total orbital angular momentum. The Laughlin functions are special cases of this ansatz for infinite solvable fields and equal pair-angular-momenta.

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“…The open shell systems are calculated using a restricted Hartree-Fock method (27), followed by a CI generated using Rumer diagram techniques (28,29). Transition moments are calculated using the dipole length operator and keeping all one center terms.…”

Section: Methodsmentioning

confidence: 99%

A theoretical study of the electronic structure and spectra of metalloporphine cations

Edwards¹,

Zerner²

1985

Can. J. Chem.

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A theoretical study is made of the electronic spectra of Mg(lI), Zn(II), and Co(II1) porphine and their TI cations using the INDOIS-CI spectroscopic model. Thc calculated electronic spectra for the neutral compounds compare wcll with experiment. The two low-lying TI cations, one of ' A , , and one of 'A,, symmetry are both examined for each of these systems. The ' A , , cations are calculated to lie lower in energy than the 'A'. cations by only 4 kcal/mol, consistent with the findings that both ions are found depending on substituents and solvent.The visible region of the spectrum of the ' A , , species is predicted to consist of three separate bands decreasing in intensity with increasing energy, while that of the 'A'. species is calculated to consist of three allowed transitions of near equal intensity, in agreement with experimental findings. In general the Soret rcgion of the %,, ions is dominated by one transition, while at least three strong bands are calculated in the Soret region for the 'A2,, ions, again in reasonable accord with experiment. Charges, ionization energies, and spin densities are reported and discussed for all compounds.

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Spin Eigenfunctions

Cited by 405 publications

References 0 publications

Initial stage of quasiparticle decay in fermionic systems

Initial stage of quasiparticle decay in fermionic systems

Special analytical solutions of the Schrödinger equation for two and three electrons in a magnetic field and ad hoc generalizations toNparticles

A theoretical study of the electronic structure and spectra of metalloporphine cations

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