Dresden 2020 – scientific programme

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HL: Fachverband Halbleiterphysik

HL 30: Poster I

HL 30.18: Poster

Tuesday, March 17, 2020, 13:30–15:45, P3

Do equidistant energy levels necessitate a harmonic potential? — •Fabian Teichert, Eduard Kuhn, and Angela Thränhardt — Institute of Physics, Technische Universität Chemnitz, 09107 Chemnitz, Germany

Experimental results from literature show energetically equidistant quantum well states in thin Bi films on surfaces, suggesting a harmonic oscillator description [1,2]. Yet is this conclusion imperative, especially considering that any measurement only yields energy levels in a finite range and with a nonzero uncertainty? Within this study we investigate whether equidistant energy levels actually necessitate a harmonic potential or whether alternative potential shapes with equidistant levels exist. First, we describe experimental results from literature by a harmonic oscillator model, obtaining a realistic size and depth of the resulting quantum well. Second, we use the shift-operator approach to calculate anharmonic non-polynomial potentials producing (partly) equidistant spectra. We discuss different potential types and interpret the possible modeling applications [3]. Finally, by applying nth order perturbation theory we show that exactly equidistant eigenenergies cannot be achieved by polynomial potentials, except by the harmonic oscillator potential.
[1] P. Kröger et al.: Physical Review B 97 (2018), 045403
[2] T. Hirahara et al.: Physical Review B 75 (2007), 035422
[3] F. Teichert et al.: arXiv:1910.12522 [quant-ph]