Akademik Veri Yönetim Sistemi
Conference of the NATO-Advanced-Study-Institute on Structure and Dynamics of Elementary Matter, Carmyuva-Kemer, Türkiye, 22 Eylül - 02 Ekim 2003, cilt.166, ss.673-675
In this study we discuss the quantum dynamics of a particle, which moves classically on the brachistochrone curve corresponding to the minimization of the time functional, in a linear gravity potential. We derive the Lagrangian and the Hamiltonian of the particle, which moves also on the brachistochrone curve by the minimization of the action functional. The solutions of the Schrodinger's equation for this Hamiltonian give the energy spectrum, and the confluent hyper-geometric functions as the wave functions. The problem combines the infinite-well and harmonic oscillator potentials. We also discuss the solutions of the Schrodinger's equation for the particle in the periodic extension of the original brachistochrone problem. We show that the band structure arised from Floquet theory and the problem is equivalent to the periodic delta-potential problem for the particle with positive energy in the limit of infinite potential.