Particle-like behaviour

Schrodinger s equation is widely known as a wave equation and the quantum formalism developed on the basis thereof is called wave mechanics. This terminology reflects historical developments in the theory of matter following various conjectures and experimental demonstration that matter and radiation alike, both exhibit wave-like and particle-like behaviour under appropriate conditions. The synthesis of quantum theory and a wave model was first achieved by De Broglie. By analogy with the dual character of light as revealed by the photoelectric effect and the incoherent Compton scattering... 

Erwin Schrodinger developed an equation to describe the electron in the hydrogen atom as having both wavelike and particle-like behaviour. Solution of the Schrodinger wave equation by application of the so-called quantum mechanics or wave mechanics shows that electronic energy levels within atoms are quantised that is, only certain specific electronic energy levels are allowed. 

The wave structure at small quantum numbers is well known as the textbook example of an harmonic oscillator. The inference is almost self evident particle-like behaviour only becomes pronounced on approaching the classical world, and changing into wave-like behaviour in the quantum domain. 

The accepted mode of interaction between a pair of electrons involves exchange of photons. Until this exchange has been logically formulated, no model of an electron can be considered adequate. As in the case of an electron there is a conflict between wave and particle models, and as before, it may be necessary to reject both points of view as too simplistic and to seek an alternative model of the photon that reflects all known properties, including wave- and particle-like behaviour. The key to the problem lies in the nature of interaction as an exchange, which implies equal participation of the emitter and absorber. Useful ideas in this direction have been formulated by several authors. 

The spectral function actually selected diagonal matrix elements Ann ( ) in a suitable one-electron basis representation - may exhibit well-defined structures reflecting the existence of highly probable one-electron excitations. Due to the Coulomb interaction, we cannot assign each excitation to an independent particle (electron or hole) added to the system with the excitation energy. Nonetheless, some of these structures can be explained approximately in terms of a particle-like behaviour, so having a quasiparticle (QP) peak. Where a second peak is required we may have what is called a satellite. 

Classical mechanics which correctly describes the behaviour of macroscopic particles like bullets or space craft is not derived from more basic principles. It derives from the three laws of motion proposed by Newton. The only justification for this model is the fact that a logical mathematical development of a mechanical system, based on these laws, is fully consistent... 

Where (pm is the maximum concentration at which flow is possible -above this solid-like behaviour will occur. q>/(pm is the volume effectively occupied by particles in unit volume of the suspension and therefore is not just the geometric volume but is the excluded volume. This is an important point that will have increasing relevance later. Now integration of Equation (3.53) with the boundary condition that as... 

The development of the quantum theory in the early twentieth century allowed predictions to be made relating to the properties and behaviour of matter and light. The electrons in matter have both wavelike and particle-like properties, and quantum theory shows that the energy of matter is quantised that is, only certain specific energies are allowed. 

The electrons in an atom surround the nucleus, but are constrained within given spatial limits, defined by atomic orbitals. Atomic orbitals describe the probability of finding an electron within a given space. We are unable to pin-point the electron at any particular time, but we have an indication that it will be within certain spatial limits. A farmer knows his cow is in a field, but, at any one time, he does not know precisely where it will be located. Even this is not a good analogy, because electrons do not behave as nice, solid particles. Their behaviour is in some respects like that of waves, and this can best be analysed through mathematics. 

Using model concentrated suspensions of polyvinyl chloride and titanium dioxide particles in a Newtonian polybutene fluid, small amplitude oscillatory shear and creep experiments were described [2]. It was shown that the gel-like behaviour at very small strain, and strain hardening at a critical strain, are caused by particle interactions and the state of particle dispersion. 

Wave-particle duality. . as first expre r.. jd quantilalively by de Brnpi , in his equalion /. = himv. wliK ii relalns the wave-like behaviour of any parlicle to ils inomijntum. 

To end this section, we briefly recall some results concerning the scattering intensity measured firom a collection of non-interacting particles like fringed micelles. For a non-spherical compact particle with dimension D in a space of dimension D, the asymptotic behaviour of the form factor is given by [16] ... 

Also the addition of metal particles, like zinc, to CPs can lead to a beneficial effect on corrosion protection from CP coatings. Olad [53-54] found out that incorporation of zinc nanoparticles and zinc micro-size particles produces effective PANI/Zn nanocomposite and PANI/Zn composite coatings on iron, respectively. The electrical conductivity of both nanocomposite and composite systems is correlated with the zinc content, and it is higher when Zn particles are nanosized. A similar behaviour has been found in the anticorrosive properties of PANI/Zn coatings because the synergetic effect of zinc nanoparticles is more than that of micro-sized particles. 

The second part treats the chemistry, structures and electrical properties of typical materials, from hydrogen bronzes to polymers via ice, hydroxides, acid sulphates, layer hydrates, inorganic ion exchangers, gels, porous media and mixed inorganic-organic polymers. These materials are compared with liquid and molten salt conductors, intercalated graphites and metal hydrides and have been chosen in order to illustrate the different behaviour of the proton it has electron-like properties in some oxides and hydrides, ion-like behaviour in some other oxides or liquid-state behaviour such as encountered in solution covered particles or pores of a gel. 

The term heavy lepton is of course self-contradictory (an oxymoron) since lepton is borrowed from the Greek for weak or light as compared with hadron for strong or heavy . The t is heavier than most known hadrons, which means that mass alone does not allow one to characterize the elementarity of a particle. In the following, the elementarity of leptons will be taken to imply their nearly point-like behaviour at least down to distances... 

It seems safe, therefore, to conclude that the r is indeed a new spin lepton, i.e. a point-like elementary particle whose behaviour is controlled by QED. In summary, the new lepton appears to have its own lepton quantum number, i.e. to be a sequential lepton, with its own neutrino (as is discussed later), and its spin coupling structure is consistent with the traditional V — A coupling of its lighter companions e and fi. It therefore seems to be a genuine recurrence in the g sequence. 

SAPs known as hydrogels are hydrophilic cross-linked polymers that swell in water. These products utilize SAP (normally in powder form) to create the absorbent core, which acts as the storage stmcture in the product. Sometimes they are called intelhgent gels because 1 g of hydrogel can absorb even up to 1000 g of water. The SAP particles usually have a sand-like feature, which is not comfortable when it mbs against skin. Also, its gel-like behaviour when wet does not produce a desirable feeling if it comes into contact with the skin. 

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