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arXiv · 1601.00902

Some studies on quantum equivalents of non-commutative operators via commutating eigenvalue relation: PT-symmetry

Biswanath Rath
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Abstract

We study quantum equivalents of non-commutative operators in quantum mechanics. Any matrix "$B$" satisfying the non-commuting relation $[A,B]\neq 0$ with "$A$", can be used via $B^{-1} AB$ to reproduce eigenvalues of "$A$". This universality relation is also equally valid for any matrix in any branch of physical or social science and also any operator involving co-ordinate$(x)$ or momentum$(p)$. Pictorially this is represented in fig. 1. Many interesting models including logarithmic potential have been considered.

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Biswanath Rath. 2015-12-20. Some studies on quantum equivalents of non-commutative operators via commutating eigenvalue relation: PT-symmetry. https://arxiv.org/abs/1601.00902

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