Russian Physics Journal

, Volume 41, Issue 5, pp 420–427 | Cite as

Quantum projection. Integration of the open Tod quantum chain

  • I. V. Shirokov
  • A. A. Drokin
Physics Of Elementary Particles And Field Theory


A quantum projection method is developed on the basis of noncommutative integration of linear differential equations and the results of M. A. Ol’shanetskii and A. M. Perelomov on the integration of classical Hamiltonian systems (projection method). The method proposed makes it possible to obtain in explicit form solutions of the quantum equations whose classical analogs can be integrated by projection. Then the semisimplicity property of the symmetry algebra of the original equation is no longer a factor. The solution basis of a Schrödinger equation with the potential of an open three-particle Tod chain is constructed as a nontrivial example.


Hamiltonian System Solution Basis Linear Differential Equation Symmetry Algebra Casimir Operator 
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© Plenum Publishing Corporation 1998

Authors and Affiliations

  • I. V. Shirokov
  • A. A. Drokin

There are no affiliations available

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