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Advances in hadronic chemistry and its applications

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Abstract

In this paper, we outline the foundations of the time invariant, non-unitary covering of quantum chemistry known as hadronic chemistry, we illustrate its validity by reviewing the exact representations of the binding energies of the Hydrogen and water molecules, and present new advances.

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Notes

  1. For example let us consider a divergent canonical series,

    $$\begin{aligned} A(k)=A(0)+k \times [A,H]/1!+k^2 \times [[A,H],H]/2!+ \cdots \longrightarrow \infty , k>1, \end{aligned}$$

    where \([A,H] = A \times H - H \times A\) is the familiar Lie product, and the operators \(A\) and \(H\) are Hermitian and sufficiently bounded. Then under the isotopic lifting the preceding series becomes

    $$\begin{aligned} {\hat{A}}(k)&={\hat{A}}(0)+k \times [A{\hat{,}H}]/1!+k^2 \times [[A{\hat{,}H}]{\hat{,}H}]/2!+ \cdots \le |N| < \infty ,\\ [A {\hat{,}H}]&= A \times {\widehat{T}} \times H - H \times \widehat{T} \times A, \end{aligned}$$

    which holds e.g. for the case \(\widehat{T} = \epsilon \times k^{-1}\) where \(\epsilon\) is sufficiently small positive definite constant. This shows that the original divergent coefficient are now turned into the convergent coefficients. Therefore, by permitting fast convergence of perturbative series, all known applications of hadronic mechanics allows much faster computations. For example, when computer uses iteration method of computation obviously due to the fast convergence of the series having isotopic element as variable it would take drastically less steps of iterations.

  2. In usual quantum chemistry the allowed approximations are \(r_{1a}\approx r_{2b}\) and \(r_{2a} \approx r_{1b}\) but since we are dealing at much shorter distances, viz. \(r_{12}\) the approximations of Eqs. (28) and (29) are in order.

  3. As described in the following paragraph it is assumed that each isoelectronium sees only one positive charge located at the nucleus of Oxygen atom.

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Acknowledgments

The financial support from The Santilli Foundation is gratefully acknowledged. I am indebted especially to Professor R. M. Santilli for his guidance and motivation during the seminar course on Hadronic Mechanics and inviting me to write this paper with valuable guidance. The author is also thankful to Mrs. Carla Santilli, Professor C. Corda and Professor R. Anderson for all the encouragement and for providing an opportunity to learn Santilli’s new mathematics and its applications. Finally the author is personally thankful to Professor A. A. Bhalekar for initiating me in this subject and providing valuable guidance and encouragement at every stage of the writing of this review paper. This work is financially supported by The Santilli Foundation and presented at the Seminar Course on Hadronic Mechanics, in International Conference of Numerical Analysis and Applied Mathematics (ICNAAM)—2012, at Kos, Greece, during 19–25 September 2012.

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  1. Department of Chemistry, Rashtrasant Tukadoji Maharaj Nagpur University, Amravati Road Campus, Nagpur, 440033, Maharashtra, India

    Vijay M. Tangde

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Tangde, V.M. Advances in hadronic chemistry and its applications. Found Chem 17, 163–179 (2015). https://doi.org/10.1007/s10698-015-9218-z

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