Quaternionic potentials in non-relativistic quantum mechanics

Leo, Stefano De; Ducati, Gisele; Nishi, C. C.

doi:10.1088/0305-4470/35/26/305

Cited by 59 publications

(49 citation statements)

References 30 publications

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“…Recent studies of quaternionic barrier [6] and well [7] potentials confirmed that the solution of Eq. (5) has to be expressed as the product of two factors: a quaternionic constant coefficient, p, and a complex exponential function, exp[z x] (z ∈ C).…”

Section: Introductionmentioning

confidence: 80%

Zeros of unilateral quaternionic polynomials

Ducati¹,

Leonardi²

2006

ELA

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Abstract. The purpose of this paper is to show how the problem of finding the zeros of unilateral n-order quaternionic polynomials can be solved by determining the eigenvectors of the corresponding companion matrix. This approach, probably superfluous in the case of quadratic equations for which a closed formula can be given, becomes truly useful for (unilateral) n-order polynomials. To understand the strehgth of this method, we compare it with the Niven algorithm and show where this (full) matrix approach improves previous methods based on the use of the Niven algorithm. For the convenience of the readers, we explicitly solve some examples of second and third order unilateral quaternionic polynomials. The leading idea of the practical solution method proposed in this work can be summarized in following three steps: translating the quaternionic polynomial in the eigenvalue problem for its companion matrix, finding its eigenvectors, and, finally, giving the quaternionic solution of the unilateral polynomial in terms of the components of such eigenvectors. A brief discussion on bilateral quaternionic quadratic equations is also presented.

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Section: Introductionmentioning

confidence: 80%

Zeros of unilateral quaternionic polynomials

Ducati¹,

Leonardi²

2006

ELA

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“…From the 106 elements given in (11), that we can rewrite in the matricial form, we can extract two different basis bases for GL(8, R) those are…”

Section: Real Matrix Conversionmentioning

confidence: 99%

The octonionic eigenvalue problem

Ducati¹

2012

J. Phys. A: Math. Theor.

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Abstract. By using a real matrix translation, we propose a coupled eigenvalue problem for octonionic operators. In view of possible applications in quantum mechanics, we also discuss the hermiticity of such operators. Previous difficulties in formulating a consistent octonionic Hilbert space are solved by using the new coupled eigenvalue problem and introducing an appropriate scalar product for the probability amplitudes.

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“…Having appropriate mathematical tools using quaternions [9,10], a lot of efforts have been made to reconstruct quantum mechanics in terms of quaternion functions during the past few decades such as those by Kaneno [11], Finkelstein and Jauch [12,13], Emch [14], Horwitz and Biedenharn [15], De Leo [16][17][18][19][20], to name a few; maybe the best-known person in this research field is Adler [21][22][23][24][25][26]. In recent times, scattering for non-relativistic and spinless quantum particles has been studied in [27][28][29] in the presence of a quaternionic Dirac delta potential in the direction proposed by De Leo [20].…”

Section: Introductionmentioning

confidence: 99%

Relativistic scattering of fermions in quaternionic quantum mechanics

Hassanabadi

Sobhani

Banerjee³

2017

Eur. Phys. J. C

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In this article, we propose a quaternionic version of the Dirac equation in the presence of scalar and vector potentials. It has been shown that in complex limit of such an equation, the complex version of this equation can be covered. After setting a quaternionic form for the Dirac delta potential, scattering due to the considered interaction has been studied. Wave functions and discontinuity conditions of the problem considered have been derived in detail. Using the continuity equation, we have found a constraint implying the conservation law of the probability current.

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Quaternionic potentials in non-relativistic quantum mechanics

Cited by 59 publications

References 30 publications

Zeros of unilateral quaternionic polynomials

Zeros of unilateral quaternionic polynomials

The octonionic eigenvalue problem

Relativistic scattering of fermions in quaternionic quantum mechanics

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