Heisenberg Uncertainty principle pulse excitation

For the ultrashort events, the question arises as to whether the Heisenberg uncertainty principle has relevance. A consequence of this principle is that in measurements of the energy ( ) of a system over a time t there is a relation between the uncertainty AE (i.e., the mean square deviation) of E and that of the time (Ar), namely AE x At h/An, where h is Planck s constant. If one wishes to measure the energy E within an accuracy of A E, the measurements must be extended over a time-interval of at least hlAn A E. This fact has implications for spectroscopy, since it affects the sharpness of spectral lines. Consider the excitation by a photon of a molecule from the ground state to an upper state. The breadth (Av) of a line in the vibrational spectrum is related to AE by the equation An = AE/A, and so is related to the duration t of the excited state by Av = l/Ant. If t is very short, A V may be appreciable and the spectral lines will appear diffuse. As an example, consider the dissociation of an iodine molecule (I2 21) by a femtosecond pulse the quantities... 

It is widely appreciated that modem NMR spectrometers use a short pulse of radiofrequency energy to excite nuclear resonances over a range of frequencies. This pulse is supplied as monochromatic radiation from the transmitter, yet the nuclear spin transitions giving rise to our spectra vary in energy according to their differing Larmor frequencies and so it would appear that the pulse will be unable to excite all resonances in the spectmm simultaneously. However, Heisenberg s Uncertainty principle tells us that an excitation pulse of duration At has associated with it a frequency uncertainty or spread of around 1/At Hz... 

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