Extended wavefunctions

In the case of one particle QO, the necessary quadrivector structure, which must adopt the extended wavefunctions, acquire a qualitative similarity to relativistic spinors [77]. In order to obtain mathematics coherence, even non-relativistic Quantum Mechanics seems that can be easily attached to a vector-like wavefunction representation, originated due to the presence of momentum and thus of KE differential operators. An idea of Levy-Leblond [78], recently quoted by Karbowski [79] can be related to this feature. 

This amounts the same as to consider normalised the total extended wavefunction. Id) ... 

This is a consequence of the characteristics of the spaces containing both, the wavefunction and their gradient, whose elements, then, should be considered square summable functions. The normalisation of the extended wavefunction O, ... 

At the same time, one can define angular momentum DF (AM DF) using the same arguments as before, taking the vector part of the resultant extended wavefunction ... 

The also so-called mass-velocity term, is mainly related to the fourth power of momentum, and thus with the operator V. The adequate operator structure will be given by a diagonal operator V = Diag l -V )= Diag A) acting on the extended wavefunctions, in this way, using Green s first theorem ... 

There can be seen that, not only the Hamilton operator could be written as a diagonal matrix, but the elements of the EH space too. It is only necessary to take into account the isomorphism between the extended wavefunction form and a diagonal structure, which can be defined employing a diagonal operator instead of the vector one used in writing equation (II) ... 

This last expression ensures the extended wavefunction norm as defined in equation (13). The same relationships as in equation (10), can be obtained with the following sequence, employing once more Green s theorem ... 

The transformed equation has the appropriate structure to be further transformed and manipulated into EH spaces. For this purpose, it is only necessary to construct an extended wavefunction like ... 

However, if we consider a plane-wave state with a spatially very extended wavefunction, then its form factor may well drop to a small value at Such a situation is the case for 6d states, as illustrated in fig. 9. It is clear, therefore, that if an appreciable amount of the magnetization density is 6d-like, then it will not be seen in form-factor measurements that are dependent on Bragg scattering. Such a density will, of course, be picked up by bulk magnetization techniques since then an integration over the whole unit cell is performed. 

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