( quantum chemistry ) and spectroscopy.

Applied quantum chemistry, specifically, orbital hybridization best describes chemical bonding in nanotubes.

Fields of specialization include biochemistry, nuclear chemistry, organic chemistry, inorganic chemistry, polymer chemistry, analytical chemistry, theoretical chemistry, quantum chemistry, environmental chemistry, and physical chemistry.

Important areas of study include chemical thermodynamics, chemical kinetics, electrochemistry, quantum chemistry, statistical mechanics, and spectroscopy.

In particular the application of quantum mechanics to chemistry is called quantum chemistry.

* COLUMBUS, ab initio quantum chemistry software

Most quantitative calculations in modern quantum chemistry use either valence bond or molecular orbital theory as a starting point, although a third approach, Density Functional Theory, has become increasingly popular in recent years.

This book helped experimental chemists to understand the impact of quantum theory on chemistry.

Modern calculations in quantum chemistry usually start from ( but ultimately go far beyond ) a molecular orbital rather than a valence bond approach, not because of any intrinsic superiority in the former but rather because the MO approach is more readily adapted to numerical computations.

Building on the founding discoveries and theories in the history of quantum mechanics, the first theoretical calculations in chemistry were those of Walter Heitler and Fritz London in 1927.

The books that were influential in the early development of computational quantum chemistry include Linus Pauling and E. Bright Wilson's 1935 Introduction to Quantum Mechanics – with Applications to Chemistry, Eyring, Walter and Kimball's 1944 Quantum Chemistry, Heitler's 1945 Elementary Wave Mechanics – with Applications to Quantum Chemistry, and later Coulson's 1952 textbook Valence, each of which served as primary references for chemists in the decades to follow.

A notable exception are certain approaches called direct quantum chemistry, which treat electrons and nuclei on a common footing.

These methods are called quantum chemistry composite methods.

Semi-empirical quantum chemistry methods are based on the Hartree – Fock formalism, but make many approximations and obtain some parameters from empirical data.

Usually, computation on a quantum computer ends with a measurement.

Several condensed matter systems are being studied with potential applications to quantum computation, including experimental systems like quantum dots, SQUIDs, and theoretical models like the toric code and the quantum dimer model.

The latter, though more rarely discussed, is interesting, as it is the suitable setting for quantum computation, whereas the former is sufficient for classical logic.

In quantum computation, entangled quantum states are used to perform computations in parallel, which may allow certain calculations to be performed much more quickly than they ever could be with classical computers.

In contrast all finite-dimensional inner product spaces over or, such as those used in quantum computation, are automatically metrically complete and hence Hilbert spaces.

For example, we cannot create backup copies of a state in the middle of a quantum computation, and use them to correct subsequent errors.

The reason for quantizing a theory is to deduce properties of materials, objects or particles through the computation of quantum amplitudes.

Major goals of quantum chemistry include increasing the accuracy of the results for small molecular systems, and increasing the size of large molecules that can be processed, which is limited by scaling considerations — the computation time increases as a power of the number of atoms.

A quantum computer is a computation device that makes direct use of quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data.

Whereas digital computers require data to be encoded into binary digits ( bits ), quantum computation uses quantum properties to represent data and perform operations on these data.

Given unlimited resources, a classical computer can simulate an arbitrary quantum algorithm so quantum computation does not violate the Church – Turing thesis.

While a classical three-bit state and a quantum three-qubit state are both eight-dimensional vectors, they are manipulated quite differently for classical or quantum computation.

In quantum computation, on the other hand, allowed operations are unitary matrices, which are effectively rotations ( they preserve that the sum of the squares add up to one, the Euclidean or L2 norm ).

( Technically, quantum operations can be probabilistic combinations of unitaries, so quantum computation really does generalize classical computation.

There are a number of quantum computing models, distinguished by the basic elements in which the computation is decomposed.

Atomic orbitals are typically categorized by n, l, and m quantum numbers, which correspond to the electron's energy, angular momentum, and an angular momentum vector component, respectively.

Still, the Bohr model's use of quantized angular momenta and therefore quantized energy levels was a significant step towards the understanding of electrons in atoms, and also a significant step towards the development of quantum mechanics in suggesting that quantized restraints must account for all discontinuous energy levels and spectra in atoms.

In states where a quantum mechanical particle is bound, it must be localized as a wave packet, and the existence of the packet and its minimum size implies a spread and minimal value in particle wavelength, and thus also momentum and energy.

In quantum mechanics, as a particle is localized to a smaller region in space, the associated compressed wave packet requires a larger and larger range of momenta, and thus larger kinetic energy.

In the quantum picture of Heisenberg, Schrödinger and others, the Bohr atom number n for each orbital became known as an n-sphere in a three dimensional atom and was pictured as the mean energy of the probability cloud of the electron's wave packet which surrounded the atom.

where X is the energy level corresponding to the principal quantum number n, type is a lower-case letter denoting the shape or subshell of the orbital and it corresponds to the angular quantum number l, and y is the number of electrons in that orbital.

The principal quantum number, n, describes the energy of the electron and is always a positive integer.

Solutions of the Dirac equation contained negative energy quantum states.

In quantum field theory, this process is allowed only as an intermediate quantum state for times short enough that the violation of energy conservation can be accommodated by the uncertainty principle.

where we use the symbol k to denote the quantum numbers p and σ of the previous section and the sign of the energy, E ( k ), and a < sub > k </ sub > denotes the corresponding annihilation operators.

A system at absolute zero still possesses quantum mechanical zero-point energy, the energy of its ground state.

Nevertheless, for convenience, there is usually some logical scheme behind the labels inside kets, such as the common practice of labeling energy eigenkets in quantum mechanics with a list of their quantum numbers.

Goldstone's theorem in quantum field theory states that in a system with broken continuous symmetry, there may exist excitations with arbitrarily low energy, called the Goldstone bosons.

It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta, entities which fit neither the classical idea of particles nor the classical idea of waves.

Classical physics draws a distinction between particles and energy, holding that only the latter exhibit waveform characteristics, whereas quantum mechanics is based on the observation that matter has both wave and particle aspects and postulates that the state of every subatomic particle can be described by a wavefunction — a mathematical expression used to calculate the probability that the particle, if measured, will be in a given location or state of motion.

* The prediction of the molecular structure of molecules by the use of the simulation of forces, or more accurate quantum chemical methods, to find stationary points on the energy surface as the position of the nuclei is varied.

The energy bands each correspond to a large number of discrete quantum states of the electrons, and most of the states with low energy ( closer to the nucleus ) are occupied, up to a particular band called the valence band.

Thus it can be interpreted without any reference to the zero-point energy ( vacuum energy ) or virtual particles of quantum fields.