September 2012
Beginner
576 pages
15h 11m
English
Content preview from Principles of Quantum Mechanics
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Appendix B
Some Supplementary Topics
B.1 FOURIER TRANSFORM
B.1.1 Fourier Series
Let us consider a periodic single valued function f(x) in the interval –π ≤ x ≤ π [such that f(x + 2π) = f(x)]. The Fourier series corresponding to f(x) is defined as
This series converges in the said interval (–π, π), if f(x) and f′(x) [= (∂f /∂x)] are continuous. Multiplying Eq. (B.1) by cos(mx) and integrating over –π to π, we get
Again multiplying (B.1) by sin (mx) and integrating over −π to π, we get
The series (B.1) may also be written in an alternative form ...
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