Revista Brasileira de Ensino de Física
Print version ISSN 1806-1117
DE VINCENZO, Salvatore. Classical-quantum versus exact quantum results for a particle in a box. Rev. Bras. Ensino Fís. [online]. 2012, vol.34, n.2, pp.1-5. ISSN 1806-1117. http://dx.doi.org/10.1590/S1806-11172012000200019.
The problems of a free classical particle inside a one-dimensional box: (i) with impenetrable walls and (ii) with penetrable walls, were considered. For each problem, the classical amplitude and mechanical frequency of the T -th harmonic of the motion of the particle were identified from the Fourier series of the position function. After using the Bohr-Sommerfeld-Wilson quantization rule, the respective quantized amplitudes and frequencies (i.e., as a function of the quantum label n ) were obtained. Finally, the classical-quantum results were compared to those obtained from modern quantum mechanics, and a clear correspondence was observed in the limit of n » τ.
Keywords : classical mechanics; particle in a box; Fourier harmonics; Heisenberg harmonics.