Where can I find a quantitative and qualitative explanation of this? In the world is someone interested in that ?
Why has a problem not been solved by the quantum mechanical approach?
As a matter of fact, if the different forms of electron orbitals form the mechanical properties of molecular bonds, it seems we can calculate these properties by the methods of quantum mechanics, applied to one atom (see ISBN: 978-3-659-48612-8 where the trajectory of theoretical particle should be understood in quantum mechanical sense , that is, as a trajectory of statistical ensemble of particles, but not a trajectory of single particle. In principle, only the form of trajectory of this ensemble is interesting, and not more.
The different quantum numbers give different forms of trajectories. These forms give information which are enough to get mechanical properties of the nanostructures which consist of a few atoms. The method is similar to Lego constructor for children.
The equations of quantum mechanics can be solved only for one-electron systems. Naturally, the properties of a material like graphene will not be well reproduced by any consideration of only one electron! Beyond that, the multiplication of interactions - electron-electron and electron-ion - makes exact solution of the Shrödinger equation impossible. At the moment, the only way to make inroads is to make certain approximations or assumptions about these interactions.
One such approach is density functional theory (DFT), in which electron-electron interactions are abstracted such that the energy of the electron system is a functional of the DENSITY of electrons, rather than the POSITION of each individual electron. Indeed, it is quite possible to use DFT to make predictions of mechanical properties - elasticity, plasticity, etc. - though of course the results are only as good as the approximations that have been made and the way they have been applied.
Philip, thanks for the clear answer. Of course, untill the theory (equation) to describe the multiparticle quantum structure will be created we can only try different approximations. The isolated particle is most likely exotic, and the matter exists only in a structural nonlocal form. Probably, the quantum nonlocality clearly indicates constant aspiration of a matter to create structure. Perhaps, essence of our problem is that, in principle, a quantum structure can not be described by way of the separate description of interaction of all its parts each other. Therefore, in a metric space it makes sense to find and carefully examine the quantum solutions that lead to various types of discreteness and neighboring locality, which are a united quantum state but rigorously isolated from each other in the metric space. These isolated discretenesses can be filled by particles or not. If the particles have filled all discretenesses of that united quantum state, the structure occurs. In this structure, the energy of each particle can be minimal if all quantum states (in discrete metric space ) have been filled with particles , that is, the creation of that quantum structure is energetically favorable (see ISBN 978-3-659-48612-8). Thus, the appearance of the structure means appearance of some type of quantization of the metric space , where each particle can be ( in one-dimensional case ) only in the interval between two boundary points ( turning points ) , where the particle changes the sign of its velocity. It seems, that such quantization in a metric space can be found, if, for example , we write the well known relation between the momentum, mass , speed (not for experimental particle, but for theoretical particle which is a statistical quantum ensemble ) p = mv = mdx / dt. These variables can be regarded as operators that act on any wave function ( in a centrally symmetric field , for a quantum oscillator , etc.). We obtain a trajectory for a quantum statistical ensemble. Thus, the orbitals take more clearer shapes which give possibility to calculate some unusual mechanical properties of graphene , the collective properties of the conductive electrons in two-dimension structures (see attached file). Of course , this approach is just one of the possibilities. It would be interesting to know if anyone is interested in this ?
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