Hermite pulse

A Gauss pulse and a polynomial multiplied by a Gauss pulse satisfy the requirements of rapid fall-off in both the time and the frequency domains. A pulse the shape of which is determined by a product of a Hermitian polynomial and a Gauss function is a Hermite pulse [Sill, War2]. Its width can be more narrow than that of a Gauss pulse. A fairly uniform rotation of z magnetization can be generated if the sum of a zeroth- and a... 

Figure 4.5 Time (right) and frequency O ft) profiles of some soft tt pulses used for narrow band excitation in NMR spectroscopy, (a) Gaussian pulse Hermite pulse and RE-BURP pulse. It is supposed that before the pulse the magnetization was in the z direction, (b) Typical magnetization trajectories for a inversion RE-BURP pulse with distinct frequency offsets. Adapted with permission from References [12,15] (Copyright 2007 American Physical Society and Elsevier).

Quantum dynamics simulations of the UV absorption spectrum and of the electronic state population dynamics of the molecule excited by a short laser pulse resonant with the transition to the bright B2u t t ) state, based on the models described in Sect. 5.3 were performed using the MCTDH method in the multi-set formalism (see Sect. 4.2.5 in Chap. 4). For the representation of the Hamiltonian and the wave function, a Hermite polynomial DVR scheme [60] was used for all the degrees of freedom. The number of SPF and primitive basis functions used in the calculations are listed in Table 5.4. Test calculations with both larger primitive and SPF bases have been... 

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