• EQAB M RABEI

      Articles written in Pramana – Journal of Physics

    • Some exactly solvable $\mathcal{PT}$ -invariant potentials with real spectra via the (extended) Nikiforov–Uvarov method

      M ABUSINI M SERHAN MOHAMMAD F AL-JAMAL AHMED AL-JAMEL EQAB M RABEI

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      The (extended) Nikiforov–Uvarov method is employed to find exact solutions of the Schrödinger operator for three $\mathcal{PT}$ -invariant potentials (periodic exponential, cotangent and $\mathcal{PT}$ -symmetric harmonic plus centrifugal). It is shown that their corresponding Schrödinger operators can exhibit real energy eigenvalues. The results are compared with similar works but with different methods. The comparisons led to Rodrigues formulas of some functions of interest. The eigenfunctions of these examples are expressed in terms of Hankel functions, Romanovski polynomials and Heun functions. The method is proved to be felicitous and leads to closed energy formulas for the potentials under study.

    • Quantisation of particle motion in dissipative harmonic environment

      EQAB M RABEI AHMED AL-JAMEL

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      In this work, the quantisation of particle propagating in a dissipative harmonic medium will be investigated using the creation and annihilation operator formalism, which is more appropriate in some fields of physics. Modelling the problem as damped harmonic oscillator, the equations of motion are then written in terms of Poisson brackets, and the Heisenberg equations are written in terms of the quantum counterpart of the Poisson bracket, known as commutators. The creation and annihilation operators are introduced and used to obtain the energy and eigenstates. Our results are in exact agreement with different quantisation approaches as in Serhan et al, J. Math. Phys. 59, 082105 (2018). The normalisable coherent states are obtained as eigenstates of the annihilation operator, which overcome the non-normalisability of these states that appeared via the dual coordinate method.

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