Optimal Control Equations for the One Dimensional Quantum Harmonic Oscillator Under the Influence of External Dipole Effects


Ayvaz M., Demiralp M.

7th International Conference on Computational Methods in Science and Engineering (ICCMSE), Rhodes, Greece, 29 September - 04 October 2009, vol.1504, pp.804-807 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1504
  • Doi Number: 10.1063/1.4771816
  • City: Rhodes
  • Country: Greece
  • Page Numbers: pp.804-807

Abstract

This study focuses on the construction of the optimal control equations for one dimensional quantum harmonic oscillator under the influence of external dipol effects and the solution of these equations by using Fluctuationlessness Theorem and a recently developed scheme called Characteristic Evolutions Method. The dipole function of the system has been taken as odd cubic spatial polynomial. Optimal control equations of the system under consideration are constructed by using expectation values of the position and the momentum operators instead of the wave and costate evolutions. It is shown that, the resulting equations are systems of ordinary differential equations and there are infinitely many ODEs. The solution strategy is based on the approximation of the expectation values for the operator products in the sense of Fluctuationlessness Theorem.