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Bulletin of the Korean Chemical Society (BKCS)

ISSN 0253-2964(Print)
ISSN 1229-5949(Online)
Volume 17, Number 2
BKCSDE 17(2)
February 20, 1996 

 
Title
π/2 Pulse Shaping via Inverse Scattering of Central Potentials
Author
Chang Jae Lee
Keywords
Abstract
It is shown that the inversion of the undamped Bloch equation for an amplitude-modulated broadband π/2 pulse can be precisely treated as an inverse scattering problem for a Schrodinger equation on the positive semiaxis. The pulse envelope is closely related to the central potential and asymptotically the wave function takes the form of a regular solution of the radial Schrodinger equation for s-wave scattering. An integral equation, which allows the calculation of the pulse amplitude (the potential) from the phase shift of the asymptotic solution, is derived. An exact analytical inversion of the integral equation shows that the detuning-independent π/2 pulse amplitude is given by a delta function. The equation also provides a means to calculate numerically approximate π/2 pulses for broadband excitation.
Page
188 - 192
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