An Introduction to the Uncertainty Principle is popular PDF and ePub book, written by Sundaram Thangavelu in 2012-12-06, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, An Introduction to the Uncertainty Principle can be Read Online from any device for your convenience.
An Introduction to the Uncertainty Principle Book PDF Summary
In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer sity of Cambridge. One result of Wiener's visit to Cambridge was his well-known text The Fourier Integral and Certain of its Applications; another was a paper by G. H. Hardy in the 1933 Journalofthe London Mathematical Society. As Hardy says in the introduction to this paper, This note originates from a remark of Prof. N. Wiener, to the effect that "a f and g [= j] cannot both be very small". ... The theo pair of transforms rems which follow give the most precise interpretation possible ofWiener's remark. Hardy's own statement of his results, lightly paraphrased, is as follows, in which f is an integrable function on the real line and f is its Fourier transform: x 2 m If f and j are both 0 (Ix1e- /2) for large x and some m, then each is a finite linear combination ofHermite functions. In particular, if f and j are x2 x 2 2 2 both O(e- / ), then f = j = Ae- / , where A is a constant; and if one x 2 2 is0(e- / ), then both are null.
Detail Book of An Introduction to the Uncertainty Principle PDF
- Author : Sundaram Thangavelu
- Release : 06 December 2012
- Publisher : Springer Science & Business Media
- ISBN : 9780817681647
- Genre : Mathematics
- Total Page : 189 pages
- Language : English
- PDF File Size : 17,8 Mb
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