Würzburg 2018 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 10: Quantum Systems, Symmetries and Scattering

MP 10.2: Talk

Thursday, March 22, 2018, 14:20–14:40, Z6 - SR 1.012

Analytic approximation for eigenvalues of a class of PT-symmetric Hamiltonians — •Oleg D Skoromnik¹ and Ilya D Feranchuk^2,3,4 — ¹Max Planck Institute for Nuclear Physics, Saupfercheckweg 1, D-69117 Heidelberg, Germany — ²Atomic Molecular and Optical Physics Research Group, Ton Duc Thang University, 19 Nguyen Huu Tho Street, Tan Phong Ward, District 7, Ho Chi Minh City, Vietnam — ³Faculty of Applied Sciences, Ton Duc Thang University, 19 Nguyen Huu Tho Street, Tan Phong Ward, District 7, Ho Chi Minh City, Vietnam — ⁴Belarusian State University, 4 Nezavisimosty Avenue, 220030, Minsk, Belarus

An analytical approximation for the eigenvalues of PT -symmetric Hamiltonian H= −d²/dx² − (ix)^є+2, є > −1 is developed via simple basis sets of harmonic-oscillator wave functions with variable frequencies and equilibrium positions. We demonstrate that our approximation provides high accuracy for any given energy level for all values of the parameter є > −1. [1] Phys. Rev. A 96, 052102 (2017)