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Position Representation of Quantum Mechanics over Riemannian Configuration Space

  • Maciej Błaszak
Chapter

Abstract

The last chapter of the book is devoted to two very important issues of the developed quantum theory. The first one is related with systematic construction of the so called position representation of quantum mechanics over an appropriate class of Riemaniann spaces in any admissible local curvilinear coordinates. In particular, for a flat space and Cartesian coordinates we reconstruct the standard quantization procedure from textbooks of quantum mechanics. The second issue of that chapter is related with quantum integrability (quantum superintegrability) and quantum separability. Actually, we present the reader a class of quantizations of classical Stäckel systems considered in previous chapters, which preserve quantum integrability, quantum superintegrability and quantum stationary separability of related quantum Hamiltonian operators.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Maciej Błaszak
    • 1
  1. 1.Division of Mathematical PhysicsFaculty of Physics UAMPoznańPoland

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