The confined breather: Quantized states from classical field theory |
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| Institution: | 1. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China;2. Department of Physics, Zhejiang Normal University, Jinhua, 321004, China;1. Department of Applied Mathematics, University of Rajshahi, Bangladesh;2. Department of Mathematics, Prairie View A&M University, Prairie View, TX, USA;3. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China;4. Department of Mathematics, Namal Institute, Talagang Road, Mianwali 42250, Pakistan;5. Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran;6. Department of Mathematics, Faculty of Science, Jiangsu University, 212013 Zhenjiang, China;7. Department of Mathematics, Obour High Institute For Engineering and Technology, 11828 Cairo, Egypt;8. Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio, Emanuele II, 39, 00186 Roma, Italy;9. Department of Computer Engineering, Biruni Univerity, Istanbul, Turkey;10. Department of Mathematics, Science Faculty, Firat University, 23119 Elazig, Turkey;11. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan |
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| Abstract: | The energy of a sine-Gordon breather moving in a square-well potential is studied. The ideally reflecting walls of the well are simulated by two trains of breathers moving with opposite velocity and opposite phase, the solution being found by use of the appropriate Bäcklund transformation. The confined breather shows discrete energy levels identical with those obtained from the Schrödinger equation for a particle confined in such a potential. The breather, however, is governed by a classical, non-linear field equation for the extended field u, which is subject to classical interpretation in contrast to the statistical interpretation of the ψ-wave of quantum mechanics. |
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