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

This article is cited in 8 papers

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.

Received: 10.06.1975


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

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