Journal of Mathematical Chemistry

, Volume 53, Issue 9, pp 1986–1996 | Cite as

The construction of the Gilmore–Perelomov coherent states for the Kratzer–Fues anharmonic oscillator with the use of the algebraic approach

  • Damian MikulskiEmail author
  • Daniel Gasperowicz
  • Jerzy Konarski
Original Paper


By applying the algebraic approach and the displacement operator to the ground state, the unknown Gilmore–Perelomov coherent states for the rotating anharmonic Kratzer–Fues oscillator are constructed. In order to obtain the displacement operator the ladder operators have been applied. The deduced SU(1, 1) dynamical symmetry group associated with these operators enables us to construct this important class of the coherent states. Several important properties of these states are discussed. It is shown that the coherent states introduced are not orthogonal and form complete basis set in the Hilbert space. We have found that any vector of Hilbert space of the oscillator studied can be expressed in the coherent states basis set. It has been established that the coherent states satisfy the completeness relation. Also, we have proved that these coherent states do not possess temporal stability. The approach presented can be used to construct the coherent states for other anharmonic oscillators. The coherent states proposed can find applications in laser-matter interactions, in particular with regards to laser chemical processing, laser techniques, in micro-machinning and the patterning, coating and modification of chemical material surfaces.


Coherent states Displacement operator Hilbert space Kratzer–Fues oscillator Ladder operators 


Conflict of interest

The authors have no financial disclosures and conflict of interest.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Damian Mikulski
    • 1
    Email author
  • Daniel Gasperowicz
    • 1
  • Jerzy Konarski
    • 2
  1. 1.Gen. Zamoyska and Helena Modrzejewska High School no. 2PoznanPoland
  2. 2.Department of Theoretical Chemistry, Faculty of ChemistryA. Mickiewicz UniversityPoznanPoland

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