Quantization for brachistochrone problem

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Yucel M. B., Unal N.

EUROPEAN PHYSICAL JOURNAL D, cilt.25, sa.2, ss.123-128, 2003 (SCI-Expanded)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 25 Sayı: 2
  • Basım Tarihi: 2003
  • Doi Numarası: 10.1140/epjd/e2003-00237-y
  • Dergi Adı: EUROPEAN PHYSICAL JOURNAL D
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
  • Sayfa Sayıları: ss.123-128
  • Akdeniz Üniversitesi Adresli: Evet

Özet

The brachistochrone curve corresponds to the minimization of the time functional. In this paper we discuss the dynamics of a massive particle, which moves classically on the brachistochrone curve under the potential V = -mgy. We derive the Lagrangian and the Hamiltonian of the particle and show that this problem corresponds to the particle in an infinite wall with a harmonic oscillator potential and the solutions of Schrodinger's equation are confluent hypergeometric functions. We also discuss the periodic potential problem for the brachistochrones and obtain the band structure of Kronig-Penney model for the particle with positive energy in a certain limit.