A geometrical interpretation of the time evolution of the Schrödinger equation for discrete quantum systems. (English) Zbl 0618.35099

The time evolution of a quantum state in the Schrödinger picture of quantum mechanics is presented as a curve in \({\mathbb{C}}P^ n\). An \((n+1)\)- state quantum system is considered semi-classically as a \({\mathbb{C}}P^ n\) bundle over three dimensional space, with structure group \(SU(n+1)/{\mathbb{Z}}_{n+1}\).


35Q99 Partial differential equations of mathematical physics and other areas of application
35J10 Schrödinger operator, Schrödinger equation
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
35A30 Geometric theory, characteristics, transformations in context of PDEs
Full Text: Numdam EuDML


[1] T. Eguchi , P. Gilkey and A. Hanson , Phys. Rep. , t. 66 , 1980 , p. 213 - 393 . MR 598586
[2] P.A.M. Dirac , The Principles of Quantum Mechanics , Oxford . University Press , 1981 , 4 th Edition. · Zbl 0012.18104
[3] N. Steenrod , The Topology of Fibre Bundles , Princeton University Press , 1951 . MR 39258 | Zbl 0054.07103 · Zbl 0054.07103
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.