The particle in the box: semiclassical, quantum and numerical solutions
The particle in a box model is a fundamental approximation to the simplest quantum system in which a particle translates through a space confined by an infinitely deep potential well. Evoking the postulates of quantum mechanics, the solution to this problem will give us the allowed energies, E, and...
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| Format: | Online |
| Language: | Portuguese |
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Universidade Estadual de Campinas
2021
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| Online Access: | https://econtents.sbu.unicamp.br/inpec/index.php/chemkeys/article/view/15963 |
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| Summary: | The particle in a box model is a fundamental approximation to the simplest quantum system in which a particle translates through a space confined by an infinitely deep potential well. Evoking the postulates of quantum mechanics, the solution to this problem will give us the allowed energies, E, and the respective wavefunctions, Y. Due to its simplicity, the particle in a box system offers a good starting point to experimentation with methods for solving differential equations that describe more complex quantum systems. In this text the particle in a box model is discussed in different perspectives. In other words, semiclassical, analytical, and numerical boxes represented using the cartesian coordinates. Moreover, the numerical methods presented are implemented in PYTHON language to further experimentation by the reader through the source code also presented at the end. |
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| ISSN: | 2595-7430 |
