Akademik Veri Yönetim Sistemi
Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi, cilt.17, sa.1-2, ss.86-93, 2001 (Hakemli Dergi)
The trajectory of classical least time or brachistochrone problem is a cycloid. In this paper we investigate the classical and the quantum mechanical solution of a massive particle, which moves classically on a such a curve. The solutions of the Schrödinger's equation are the parabolic cyclinder functions. Energy eigenvalues and eigenfunctions of the Brachistochrone problem of the massive particle in the potential V=-mgy are quantized. In certain limits, the solutions of the Brachistochrone problem in quantum mechanics reduce to harmonic oscillator and infinite-well potentials.