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<p>In this paper, we investigate the Schrödinger equation within the Von Roos formalism for a quantum system characterized by a position-dependent effective mass. Specifically, we consider a squared hyperbolic-cotangent potential and an effective mass described by a squared hyperbolic-secant profile. Using the Nikiforov–Uvarov (NU) method, we derive the eigenfunctions and corresponding energy eigenvalues of the system. Employing the recurrence relations of Jacobi polynomials, we construct the ladder operators and demonstrate that the system exhibits a dynamical symmetry governed by the su(1,1) Lie algebra. We further express the eigenstates in terms of the irreducible representations of this algebra. Finally, we analyze the time evolution of the coherent states associated with this symmetry and compute both the expectation value of the energy and the position-momentum uncertainty relation<i>.</i></p>

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su(1,1) Coherent State of Position-dependent Effective Mass Model for a Type of the Pöschl-Teller Quantum Potential and Time Evolution Uncertainty Relation

  • 期刊论文

  • 发表日期：

    2026年3月4日

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  • L. Z. Namvar,
  • H. Panahi,
  • A. Najafizade

摘要

In this paper, we investigate the Schrödinger equation within the Von Roos formalism for a quantum system characterized by a position-dependent effective mass. Specifically, we consider a squared hyperbolic-cotangent potential and an effective mass described by a squared hyperbolic-secant profile. Using the Nikiforov–Uvarov (NU) method, we derive the eigenfunctions and corresponding energy eigenvalues of the system. Employing the recurrence relations of Jacobi polynomials, we construct the ladder operators and demonstrate that the system exhibits a dynamical symmetry governed by the su(1,1) Lie algebra. We further express the eigenstates in terms of the irreducible representations of this algebra. Finally, we analyze the time evolution of the coherent states associated with this symmetry and compute both the expectation value of the energy and the position-momentum uncertainty relation.