dorsal/arxiv
View SchemaAnalysis of Superoscillatory Wave Functions
| Authors | M. S. Calder, A. Kempf |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0405065 |
| URL | https://arxiv.org/abs/quant-ph/0405065 |
| DOI | 10.1063/1.1825076 |
| Journal | J.Math.Phys. 46 (2005) 012101 |
Abstract
Surprisingly, differentiable functions are able to oscillate arbitrarily faster than their highest Fourier component would suggest. The phenomenon is called superoscillation. Recently, a practical method for calculating superoscillatory functions was presented and it was shown that superoscillatory quantum mechanical wave functions should exhibit a number of counter-intuitive physical effects. Following up on this work, we here present more general methods which allow the calculation of superoscillatory wave functions with custom-designed physical properties. We give concrete examples and we prove results about the limits to superoscillatory behavior. We also give a simple and intuitive new explanation for the exponential computational cost of superoscillations.
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"abstract": "Surprisingly, differentiable functions are able to oscillate arbitrarily\nfaster than their highest Fourier component would suggest. The phenomenon is\ncalled superoscillation. Recently, a practical method for calculating\nsuperoscillatory functions was presented and it was shown that superoscillatory\nquantum mechanical wave functions should exhibit a number of counter-intuitive\nphysical effects. Following up on this work, we here present more general\nmethods which allow the calculation of superoscillatory wave functions with\ncustom-designed physical properties. We give concrete examples and we prove\nresults about the limits to superoscillatory behavior. We also give a simple\nand intuitive new explanation for the exponential computational cost of\nsuperoscillations.",
"arxiv_id": "quant-ph/0405065",
"authors": [
"M. S. Calder",
"A. Kempf"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1063/1.1825076",
"journal_ref": "J.Math.Phys. 46 (2005) 012101",
"title": "Analysis of Superoscillatory Wave Functions",
"url": "https://arxiv.org/abs/quant-ph/0405065"
},
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