Define Quantum mechanics ?
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Quantum Mechanics
- Albert Thomas FromholdJr., in Encyclopedia of Physical Science and Technology (Third Edition), 2003
IX.B Quantum Mechanics Approach
Quantum mechanics permits a rationalization of the classically unexplainable observations just described. Even neglecting the ordinary Coulomb repulsion between electrons, there remains a quantum mechanical tendency for electrons to remain separated. This tendency can be treated within the framework of what is called the Pauli exclusion principle, which states that no two electrons in a system can have the same set of quantum numbers. Practically speaking, this requires higher and higher average kinetic energies for the electrons as the electron density increases. This explains why adjacent atoms resist electron-cloud overlap, even though the electron cloud otherwise would be expected to be rather soft and easily deformed under compression, and so accounts for the hard-sphere view of atoms in a crystal lattice.
The unimpeded motion of electrons moving through a lattice of such hard-sphere atoms in a solid can be understood from the wavelike properties of the electron. Even classically, it can be shown that the collective scattering of waves from a periodic array of scattering centers differs quite dramatically from the scattering of waves from a random array of scattering centers. The difference between these two situations is that a random array leads to random phases between the scattered wavefronts whereas phase coherence between the scattered wavefronts is possible if the scattering centers are located in a periodic array. (Indeed, X-ray diffraction by crystalline solids hinges on phase coherence.) In the random-array case, movement of an incident wave through the array is grossly impeded due to the partial cancellation of wavefronts having random phase with respect to one another; in the periodic array case, propagation of the wavefront becomes quite possible.
Even in the periodic case, however, there are situations in which propagation is retarded, as when a portion of the wavefront reflected from one plane of the crystalline array is superimposed upon and has a 180° phase difference with respect to another portion of the wavefront reflected from a different plane of the array. Such waves interfere destructively. Propagation, on the other hand, is enabled by a constructive interference of the scattered waves in the direction of propagation.
These facts of classical wave propagation are applicable immediately to electron propagation in solids once it is admitted that electrons have a wavelike character. Thus, it can be stated that due to the wavelike properties of electrons, the perfectly periodic array of atoms in a solid may not scatter electrons out of their straight-line path. In this sense, the periodic array may be considered to offer no resistance whatsoever to electron motion, thereby rationalizing the long, mean free paths for electrons in single, strain-free crystals of high purity held at low temperatures.
The emergent picture is that electrical resistance is not due to the scattering of electrons by the atoms of the periodic array per se but by the departures from periodicity in the crystalline array. Such departures from periodicity are provided by impurities, vacancies, strained regions, dislocations, and grain boundaries and also by thermal fluctuations of the atom array. Increased scattering at higher temperatures due to temperature-dependent thermal fluctuations in the lattice can be shown to lead to the linear temperature-dependence of the resistivity of metals. The residual resistance at extremely low temperatures is due to scattering from the impurity atoms and structural defects. A quantum mechanical approach involving the Schrödinger equation, based as it is on the wavelike behavior of particles, provides a suitable framework for rationalizing and treating these varied contributions to the electron resistivity of metals.
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.
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