Quantum Mechanical Model

Werner Heisenberg hoped that he could modify quantum physics in such a way that when the parameters were on the scale of everyday objects it would look just like classical physics, but when the parameters were pulled down to the atomic scale the discontinuities seen in things like the widely spaced frequencies of the visible hydrogen bright line spectrum would  come back into sight. He wrote an equation that is the quantum mechanical analogue for the classical computation of intensities. Although Heisenberg did not know it at the time, the general format of his new way of working with quantum theoretical calculations can serve as a recipe for two matrices and how to multiply them. Max Born puzzled over the equations and the non-commuting equations that Heisenberg had found troublesome and disturbing. After several days he realized that these equations amounted to directions for writing out matrices. Paul Dirac decided that the essence of Heisenberg's work lay in every feature that Heisenberg had originally found problematical -- the fact of non-commutativity such as that between multiplication of momentum matrix by a displacement matrix and multiplication of a displacement matrix by a momentum matrix. The insight led Dirac in new and productive directions. 

The most recent model of the atom is known as the Quantum Atomic Model.

It is based on quantum mechanics. When quantum solutions to quantum equations are combined, it is known as quantum numbers. Quantum numbers are used to find probable positions and locate the electron in an atom. There are four types of sub-level. The sub-level within the energy level where the electron is most likely to be found is identified by the azimuthal quantum number. The type of the sub-level will depend on the number of orbitals in a sub-level. The electron-spin number is used when distinguishing between two electrons in a sub-level. The electron-spin number is used when distinguishing between two electrons in an orbital. There are two possible electron-spin quantum numbers and these are ½+ and ½-.  

Quantum mechanics (QM) or quantum physics or quantum theory, is a branch of physics that provides a mathematical description of much of the wave-like behavior and interactions of energy and matter that depart from classical mechanics at the atomic and subatomic scales. In advanced topics of QM, some of these behaviors are macroscopic and emerge at very low or very high energies or temperatures. The name derives from the observation that some physical quantities—such as the angular momentum of, or more generally the action of, for example, an electron bound into an atom or molecule—can be changed only by discrete amounts, or quanta as multiples of the Planck constant, rather than being capable of varying continuously or by any arbitrary amount. An electron bound in an atomic orbital has quantized values of angular momentum while an unbound electron does not exhibit quantized energy levels but the latter is associated with a short quantum mechanical wave length. In the context of QM, the wave–particle duality of energy and matter and the uncertainty principle provide a unified view of the behavior of photons,electrons and other atomic-scale objects.A body of scientific principles describing the behavior of matterand its interactions on the atomic and subatomic scales are also known as the quantum mechanics. Classical physics was unable to explain certain phenomena just before 1900. Coming to terms with these limitations of classical physics led to the development of quantum mechanics in the early decades of the 20th century. Humans are accustomed to reasoning about the world on a scale where classical physics is an excellent approximation. That is why human minds somehow are having a hard time to understand the principles of quantum mechanics. Quantum mechanics is counterintuitive or it is not in accordance with what would naturally be assumed or expected.Photons or discrete units of light, behave in some ways like particles and in other ways like waves. A discontinuous and color coded sequences are formed by photon energies. The laws of quantum mechanics are the ones who predict the energies, the colors, and the spectral intensities of electromagnetic radiation. The pairs of particles can be created as entangled twins -- which means that an action that pins down one characteristic of one particle will instantaneously pin down the same or other characteristic of its entangled twin, regardless of the distance separating the both of them.

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