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Article overview
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Analysis of Superoscillatory Wave Functions | M.S. Calder
; A. Kempf
; | Date: |
13 May 2004 | Journal: | J.Math.Phys. 46 (2005) 012101 | Subject: | quant-ph hep-th | 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. | Source: | arXiv, quant-ph/0405065 | Services: | Forum | Review | PDF | Favorites |
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