Fourth Painlevé and Ermakov equations: quantum invariants and new exactly-solvable time-dependent Hamiltonians

@article{Zelaya2020FourthPA,
  title={Fourth Painlev{\'e} and Ermakov equations: quantum invariants and new exactly-solvable time-dependent Hamiltonians},
  author={Kevin Zelaya and Ian Marquette and V{\'e}ronique Hussin},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2020}
}
In this work, we introduce a new realization of exactly-solvable time-dependent Hamiltonians based on the solutions of the fourth Painleve and the Ermakov equations. The latter is achieved by introducing a shape-invariant condition between an unknown quantum invariant and a set of third-order intertwining operators with time-dependent coefficients. The new quantum invariant is constructed by adding a deformation term to the well-known parametric oscillator invariant. Such a deformation depends… 

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