Quantum mechanics described

Quantum Mechanics Describes Matter in Terms of Wavefunctions and Energy Levels. Physical Measurements are Described in Terms of Operators Acting on Wavefunctions... 

Quantum mechanics, which replaced the old quantum theory, was not easy to interpret. It conceived of both light and particles as having a dual nature. They were sometimes observed to be waves and sometimes particles, depending on the type of experiment that one performed. For example, the electron seemed sometimes to be a particle and sometimes a packet of waves. Furthermore, quantum mechanics described the subatomic world in terms of probabilities. 

Quantum mechanics describes molecules in terms of interactions among nuclei and electrons, and molecular geometry in terms of minimum energy arrangements of nuclei. All quantum mechanical methods ultimately trace back to the Schrodinger equation, which for the special case of hydrogen atom (a single particle in three dimensions) may be solved exactly. ... 

In addition to operators corresponding to each physically measurable quantity, quantum mechanics describes the state of the system in terms of a wavefunction F that is a function of the coordinates qj and of tune t. The function l F/(qj,t)l2 = P P gives the probability density for observing the coordinates at the values qj at time t. For a many-particle system such as the H2O molecule, the wavefunction depends on many coordinates. For the H2O example, it depends on the x, y, and z (or r,0, and < )) coordinates of the ten... 

Schrodinger s picture of quantum mechanics describe any object (for example, an electron) by its wavefunction, fix). The wavefunction itself is not directly observable, but it contains information about all possible observations because of the following two properties. 

The hope of understanding the concept of molecular structure quantum-mechanically would obviously be at its most realistic for the smallest of molecules at the absolute zero of temperature. However, under these conditions completely different pictures emerge for the molecule in, either total isolation, or in a macroscopic sample. In the latter case the molecule appears embedded in a crystal, which is quantum-mechanically described by a crystal hamiltonian with the symmetry of the crystal lattice. The isolated molecule has a spherically symmetrical hamiltonian. The two models can obviously not define the same quantum molecule. 

Quantum mechanics describes a molecular system in which both electrons, ... 

The general point against the suggestion that molecular chemistry can be reduced to quantum mechanics is that the decision when and where to suppress the interaction with the environment is not something that can be derived from quantum mechanics— this is where Gell-Mann s "chemical questions being asked" (mentioned earlier) enter the discussion. But it is these decisions that, as it were, abstract objects out of the quantum mechanical formalism. Quantum mechanics describes the material world, in principle, as one whole. Within quantum mechanics an object can only be defined in terms of its relations to its environment. To separate out objects from this whole requires a justification that lies outside the principles of quantum mechanics. Because "the" environment consists of the rest of the universe, it can never be given a precise description and must therefore be replaced by a model environment that mimics aspects of the real situation. 

For the p-p reaction the electrostatic and strong forces are significant. Since E-kin C / -/ pot,max, classical physics states that, although the resultant 2p nucleus would be energetically favourable, the two protons cannot approach one another to within a separation r. However, quantum mechanics describes the proton as a wavefunction 4> given by the solution of the Schrodinger equation... 

The formation of covalent chemical bonds in a molecule is quantum mechanically described by the overlap of atomic orbitals (AO) centered at different atoms... 

Quantum mechanics describes system behavior in terms of operators that represent measurable quantities, their eigenfunctions, which describe possible states of the system, and their eigenvalues, which correspond to allowable values of the measurable. If the system is presumed best described in terms of a specification of the system energy, then one looks for states [f) that are eigenfunctions of the molecular Hamiltonian operator H. That is, one solves the problem... 

Quantum mechanics describes and defines the behavior of electrons in atoms. One of the rules of quantum behavior is that electrons are constrained to specific locales known as orbitals within the structure of an atom and are not allowed to exist at the boundaries of those locales. An observable property called quantum mechanical tunneling occurs, however, which permits electrons to move from one locale to another across the orbital boundaries. In scanning probe microscopy the miniscule electrical current due to quantum mechanical tunneling between the atoms at a surface and the atoms at the tip of an atomic-scale probe is measured as a function of their relative positions. This provides a corresponding atomic scale map of the surface structure. 

Quantum mechanics describes the structure of atoms as a very small, dense nucleus of massive protons and neutrons, surrounded by a cloud of electrons that is 100,000 times greater in diameter than the nucleus. The electron cloud is therefore very diffuse. The electrons in a neutral atom are equal in number to the protons contained in the nucleus, and are confined to specific three-dimensional regions, called orbitals, around the nucleus, and are allowed to have only very specific energies according to the orbitals they occupy. At this scale of operation, a scanning probe microscope measures the... 

Quantum mechanics describes electrons in terms of their wavelike properties. 

Figure 12 Model of the 360-atom Si(lOO) surface used in the MD simulations. Shaded circles represent quantum mechanically described atoms white circles, empirical atoms cross-hatched circles, empirical atoms subjected to temperature control and black circles, empirical atoms held in fixed positions throughout the simulations. Adapted from Ref. 287.

Quantum mechanics describes the change of state which occurs in an A-B collision in terms of the wave functions of the interacting particles the wave function for the pair changes from B) B). 

With a role similar to Newton s second law in classical mechanics, the SchrOdinger equation in quantum mechanics describes how the wavefunction evolves in time ... 

Quantum mechanics describes the motions of subatomic particles like electrons and nuclei in terms of wavefunctions and the Hamiltonians that govern them, much as Newton s physics describes the trajectories of mechanical systems like the planets, and the forces that govern them. In a deductive chemistry, physicists and chemists would apply quantum mechanics to atoms and molecules just as Newton and his... 

Yet it was not obvious, and more to the point, I would argue that it could not have been obvious, which approach was superior either conceptually or with respect to the pragmatics of computation. Precisely because quantum mechanics was an utterly novel theoretical framework, the absence of direct results of the Schrodinger equation entailed that no one could be certain how quantum mechanics described molecular systems sans approximations. Decisions regarding which approximation techniques to use were necessary, and they necessarily relied on information strictly outside the boimdaries of quantum theory. Initial efforts were constrained to a... 

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