XXXIX Workshop on Geometric Methods in Physics | 19.06–25.06.2022 |

XI School on Geometry and Physics | 27.06–1.07.2022 |

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In order to secure the right conditions for our Workshop we have decided to exceptionally move (only for this
year's meeting) the site of our Workshop to the campus of our University in Białystok.
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## Kalpana Biswas## Closed quasi algebra for position dependent effective massLewis-Riesenfeld phase-space invariant (LRI) method is an effective tool for the construction of exact solutions of time-dependent quantum systems. The key feature of the construction mechanism lies in the construction of constituent operators, which form a closed quasi-algebra with respect to the Hamiltonian of the system. Linear combination of the constituent operators is the required invariant operator. Up to a time-dependent phase-factor, the eigenstates of the LRI operator satisfy the time-dependent Schrödinger equation. In my talk, I shall demonstrate the construction of the closed quasi-algebra with respect to the Hamiltonian for most general position-dependent effective mass (PDEM) systems. It turns out that, in order to have a finite-dimensional algebra, the forms of the allowed external potential depend on the choice of the PDEM. As a byproduct of our study, we shall construct the coherent state structure for the PDEM system. |

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University of Bialystok |

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