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 TMF: Year: Volume: Issue: Page: Find

 TMF, 1976, Volume 26, Number 3, Pages 414–418 (Mi tmf3241)

Derivation of the Schrödinger equation from scale invariance

V. Ya. Kreinovich

Abstract: It is shown that ff one postulates an equation of nonrelativistic quantum mechanics in the form $\partial\psi/\partial t=f(V,\psi,\psi^*)$, where $V$ is the potential energy, and requires that this equation, like the action (of the usual form) be invariant under the group of transformations $\mathbf x\to\lambda\mathbf x$, $t\to\mu(\lambda)t$, and also imposes certain other weak restrictions, these conditions uniquely lead to the Schrödinger equation.

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English version:
Theoretical and Mathematical Physics, 1976, 26:3, 282–285

Bibliographic databases:

Citation: V. Ya. Kreinovich, “Derivation of the Schrödinger equation from scale invariance”, TMF, 26:3 (1976), 414–418; Theoret. and Math. Phys., 26:3 (1976), 282–285

Citation in format AMSBIB
\Bibitem{Kre76} \by V.~Ya.~Kreinovich \paper Derivation of the Schr\"odinger equation from scale invariance \jour TMF \yr 1976 \vol 26 \issue 3 \pages 414--418 \mathnet{http://mi.mathnet.ru/tmf3241} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=449261} \transl \jour Theoret. and Math. Phys. \yr 1976 \vol 26 \issue 3 \pages 282--285 \crossref{https://doi.org/10.1007/BF01032102}