Translations in quantum mechanics revisited. The point spectrum case

Martínez-Pérez, Armando; Torres-Vega, Gabino

doi:10.1139/cjp-2016-0373

Cited by 5 publications

(10 citation statements)

References 15 publications

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“…with χ 1 v; j ðÞ and χ 2 v; j ðÞ given in Eqs. 7and (8), and some properties of these definitions follow. There is a plot of χ 1 v; j ðÞ in Figure 2.…”

Section: Exact First-order Finite Differences Derivative For the Expomentioning

confidence: 99%

Exact Finite Differences for Quantum Mechanics

Martínez-Pérez¹,

Torres-Vega²

2018

Numerical Simulations in Engineering and Science

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We introduce a finite difference derivative, on a non-uniform partition, with the characteristic that the derivative of the exponential function is the exponential function itself, times a constant, which is similar to what happens in the continuous variable case. Aside from its application to perform numerical computations, this is particularly useful in defining a quantum mechanical discrete momentum operator.

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“…with χ 1 v; j ðÞ and χ 2 v; j ðÞ given in Eqs. 7and (8), and some properties of these definitions follow. There is a plot of χ 1 v; j ðÞ in Figure 2.…”

Section: Exact First-order Finite Differences Derivative For the Expomentioning

confidence: 99%

Exact Finite Differences for Quantum Mechanics

Martínez-Pérez¹,

Torres-Vega²

2018

Numerical Simulations in Engineering and Science

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“…This can be seen as having the same function but now the domain has changed, it was translated by the amount u and the function is now evaluated at the new points of the domain, a continuous translation [10].…”

Section: Eigenvalues and Eigenvectorsmentioning

confidence: 99%

Exact Finite Differences. The Derivative on Non Uniformly Spaced Partitions

Martínez-Pérez

Torres-Vega

2017

Symmetry

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“…The inverse of this matrix is just the integration operation. These are interesting subjects by itself, but they are also of interest in the quantum physics realm [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Matrices Which are Discrete Versions of Linear Operations

Martínez-Pérez¹,

Vega²

2018

Matrix Theory - Applications and Theorems

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We introduce and study a matrix which has the exponential function as one of its eigenvectors. We realize that this matrix represents a set of finite differences derivation of vectors on a partition. This matrix leads to new expressions for finite differences derivatives which are exact for the exponential function. We find some properties of this matrix, the induced derivatives and of its inverse. We provide an expression for the derivative of a product, of a ratio, of the inverse of vectors, and we also find the equivalent of the summation by parts theorem of continuous functions. This matrix could be of interest to discrete quantum mechanics theory.

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Translations in quantum mechanics revisited. The point spectrum case

Cited by 5 publications

References 15 publications

Exact Finite Differences for Quantum Mechanics

Exact Finite Differences for Quantum Mechanics

Exact Finite Differences. The Derivative on Non Uniformly Spaced Partitions

Matrices Which are Discrete Versions of Linear Operations

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