超振荡粒子的奇异性质
Unusual Properties of Superoscillating Particles
摘要：
人们发现函数的局部振荡速度比它们的傅里叶变换所暗示的要快得多--这种现象被称为超振荡。这里，我们考虑量子力学中的超振荡波函数的情况。我们发现，他们拥有相当不寻常的性质，提高测量理论，热力学和信息理论的问题。我们明确确定的波函数与最显着的超振荡，连同他们的标度行为。我们还讨论了如何产生超振荡波函数的问题。
英文摘要：
It has been found that functions can oscillate locally much faster than their Fourier transform would suggest is possible - a phenomenon called superoscillation. Here, we consider the case of superoscillating wave functions in quantum mechanics. We find that they possess rather unusual properties which raise measurement theoretic, thermodynamic and information theoretic issues. We explicitly determine the wave functions with the most pronounced superoscillations, together with their scaling behavior. We also address the question how superoscillating wave functions could be produced.
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