摘要 We present a generalization of the representation

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論文資訊

• 類型：已發表論文
• 日期：2010

摘要

We present a generalization of the representation in plane waves of Dirac delta, delta(x)=(1/2 pi)integral(infinity)(- infinity)e(-ikx)dk, namely, delta(x)=[(2-q)/2 pi]integral(infinity)(- infinity)e(q)(-ikx)dk, using the non-extensive-統計-mechanics q- exponential function, e(q)(ix)equivalent to1+(1-q)ix with e(1)(ix)equivalent to e(ix), x being any real number, for real values of q within the interval [1,2[. Concomitantly, with the development of these new representations of Dirac delta, we also present two new families of representations of the transcendental number Incidentally, we remark that the q-plane wave form which emerges, namely, e(q)(ikx), pi. is normalizable for 1 < q < 3, in contrast to the standard one, e(ikx), which is not.

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