To allow wave functions to extend to infinity, we will expand the interval used
Standard Fourier Series | |
Standard Fourier Series | |
redefine coefficient | |
f stays the same | |
but is rewritten in new A and dk | |
result | |
result |
This is just the extension of the Fourier series to all .
If is normalized, then will also be normalized with this (symmetric) form of the Fourier Transform. Thus, if is a probability amplitude in position-space, can be a probability amplitude (in k-space).
Jim Branson 2013-04-22