Using Mathematical Software To Introduce Fourier Transforms in Physical Chemistry To Develop Improved Understanding of Their Applications in Analytical Chemistry
| Autor: | Jeb S. Kegerreis, Tierney C. Miller, John N. Richardson |
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| Rok vydání: | 2015 |
| Předmět: |
Uncertainty principle
010405 organic chemistry 05 social sciences Analytical chemistry 050301 education Context (language use) General Chemistry Particle in a box 01 natural sciences 0104 chemical sciences Education symbols.namesake Fourier transform Transformation (function) Frequency domain Mathematical software symbols Physical chemistry Instrumentation (computer programming) 0503 education Mathematics |
| Zdroj: | Journal of Chemical Education. 93:299-303 |
| ISSN: | 1938-1328 0021-9584 |
| Popis: | This manuscript presents an exercise that utilizes mathematical software to explore Fourier transforms in the context of model quantum mechanical systems, thus providing a deeper mathematical understanding of relevant information often introduced and treated as a “black-box” in analytical chemistry courses. The exercise is given to undergraduate students in their third year during physical chemistry, thus providing a theoretical foundation for the subsequent introduction of such material in analytical instrumentation courses. With the reinforcement of familiar concepts such as the Heisenberg Uncertainty Principle, classical correspondence, and linear combinations in the context of both position and momentum space for a particle in a box, a better understanding of the mathematical implications of the Fourier transform is fostered. Subsequent analysis of a time-dependent function constructed via a linear combination and its transformation to the frequency domain provides a practical example relating to the ... |
| Databáze: | OpenAIRE |
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