Publication
Classical-quantum versus exact quantum results for a particle in a box
| Summary: | 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. |
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| Main Authors: | De Vincenzo,Salvatore |
| Subject: | classical mechanics particle in a box Fourier harmonics Heisenberg harmonics |
| Year: | 2012 |
| Country: | Brazil |
| Document type: | report |
| Access type: | open access |
| Associated institution: | IBICT |
| Language: | English |
| Origin: | Oasisbr |
| Summary: | 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. |
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