Algebraic Function Operator Expectation Value Based Quantum Eigenstate Determination: A Case of Twisted or Bent Hamiltonian, or, a Spatially Univariate Quantum System on a Curved Space

Baykara N. A.

International Conference of Computational Methods in Sciences and Engineering (ICCMSE), Athens, Greece, 20 - 23 March 2015, vol.1702 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1702
  • Doi Number: 10.1063/1.4938948
  • City: Athens
  • Country: Greece


Recent studies on quantum evolutionary problems in Demiralp's group have arrived at a stage where the construction of an expectation value formula for a given algebraic function operator depending on only position operator becomes possible. It has also been shown that this formula turns into an algebraic recursion amongst some finite number of consecutive elements in a set of expectation values of an appropriately chosen basis set over the natural number powers of the position operator as long as the function under consideration and the system Hamiltonian are both autonomous. This recursion corresponds to a denumerable infinite number of algebraic equations whose solutions can or can not be obtained analytically. This idea is not completely original. There are many recursive relations amongst the expectation values of the natural number powers of position operator. However, those recursions may not be always efficient to get the system energy values and especially the eigenstate wavefunctions. The present approach is somehow improved and generalized form of those expansions. We focus on this issue for a specific system where the Hamiltonian is defined on the coordinate of a curved space instead of the Cartesian one.