quantum

In quantum mechanics, where all particle momenta are associated with waves, it is the formation of such a wave packet which localizes the wave, and thus the particle, in space.

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.

The new quantum mechanics did not give exact results, but only the probabilities for the occurrence of a variety of possible such results.

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.

In X-ray notation, the principal quantum number is given a letter associated with it.

A given ( hydrogen-like ) atomic orbital is identified by unique values of three quantum numbers: n, l, and m < sub > l </ sub >.

The rules restricting the values of the quantum numbers, and their energies ( see below ), explain the electron configuration of the atoms and the periodic table.

The stationary states ( quantum states ) of the hydrogen-like atoms are its atomic orbitals.

The quantum number n first appeared in the Bohr model where it determines the radius of each circular electron orbit.

In modern quantum mechanics however, n determines the mean distance of the electron from the nucleus ; all electrons with the same value of n lie at the same average distance.

Because of the quantum mechanical nature of the electrons around a nucleus, atomic orbitals can be uniquely defined by a set of integers known as quantum numbers.

These quantum numbers only occur in certain combinations of values, and their physical interpretation changes depending on whether real or complex versions of the atomic orbitals are employed.

The quantum numbers, together with the rules governing their possible values, are as follows:

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

The azimuthal quantum number,, describes the orbital angular momentum of each electron and is a non-negative integer.

The magnetic quantum number,, describes the magnetic moment of an electron in an arbitrary direction, and is also always an integer.

Alpha decay, like other cluster decays, is fundamentally a quantum tunneling process.

Classically, it is forbidden to escape, but according to the ( then ) newly-discovered principles of quantum mechanics, it has a tiny ( but non-zero ) probability of " tunneling " through the barrier and appearing on the other side to escape the nucleus.

In particle physics, antimatter is material composed of antiparticles, which have the same mass as particles of ordinary matter but have opposite charge and quantum spin.

Solutions of the Dirac equation contained negative energy quantum states.

A unified interpretation of antiparticles is now available in quantum field theory, which solves both these problems.