On the delta function normalization of the wave functions of the aharonov-bohm scattering of a dirac particle

Araujo, Vanilse S.; Coutinho, Francisco Antônio Bezerra; Perez, J. Fernando

doi:10.1590/s0103-97332002000300027

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The Location Of the Continuous Spectrum And Its Normalization1

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2020

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“…However, as stressed above, one has to correctly normalize the u E (r). This involves the difficult evaluation of divergent integrals to show that the resulting mathematical objects are δ functions [3, p. 237] [4,5], that is, that in fact they obey equation (13). The purpose of this article is to show ways of performing these difficult calculations.…”

Section: The Location Of the Continuous Spectrum And Its Normalizationmentioning

confidence: 99%

The normalization of wave functions of the continuous spectrum

Amaku

Coutinho

Toyama

2020

Rev. Bras. Ensino Fís.

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Section: The Location Of the Continuous Spectrum And Its Normalizationmentioning

confidence: 99%

The normalization of wave functions of the continuous spectrum

Amaku

Coutinho

Toyama

2020

Rev. Bras. Ensino Fís.

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Dependence of s‐waves on continuous dimension: The quantum oscillator and free systems

Wolf

Aceves-de-la-Cruz

2006

Fortschritte der Physik

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Wavefunctions with rotational symmetry (i.e., zero angular momentum) in D dimensions, are called s‐waves. In quantum quadratic systems (free particle, harmonic and repulsive oscillators), their radial parts obey Schrödinger equations with a fictitious centrifugal (for integer D ≥ 4) or centripetal (for D = 2) potential. These Hamiltonians close into the three‐dimensional Lorentz algebra so(2,1), whose exceptional interval corresponds to the critical range of continuous dimensions 0 < D < 4, where they exhibit a one‐parameter family of self‐adjoint extensions in ℒ︁2(ℜ︁+). We study the characterization of these extensions in the harmonic oscillator through their spectra which – except for the Friedrichs extension – are not equally spaced, and we build their time evolution Green function. The oscillator is then contracted to the free particle in continuous‐D dimensions, where the extension structure is mantained in the limit of continuous spectra. Finally, we compute the free time evolution of the expectation values of the Hamiltonian, dilatation generator, and square radius between three distinct sets of ‘heat’‐diffused localized eigenstates. This provides a simple group‐theoretic description of the purported contraction/expansion of Gaussian‐ring s‐waves in D > 0 dimensions.

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On the delta function normalization of the wave functions of the aharonov-bohm scattering of a dirac particle

Cited by 2 publications

References 3 publications

The normalization of wave functions of the continuous spectrum

The normalization of wave functions of the continuous spectrum

Dependence of s‐waves on continuous dimension: The quantum oscillator and free systems

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