First quantization
Encyclopedia
A first quantization of a physical system is a semi-classical
treatment of quantum mechanics
, in which particles or physical objects are treated using quantum wave functions but the surrounding environment (for example a potential well
or a bulk electromagnetic field
or gravitational field
) is treated classically. First quantization is appropriate for studying a single quantum-mechanical system being controlled by a laboratory
apparatus
that is itself large enough that classical mechanics
is applicable to most of the apparatus.
First quantization is the subject studied in most undergraduate quantum mechanics courses, and in which the Schrodinger Equation
and Heisenberg matrix mechanics
(together with bra-ket notation
) are most simply applied. It may be contrasted with Second quantization, which includes quantum-mechanical uncertainty effects in all aspects of an experiment including the controlling fields and boundary conditions.
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
treatment of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
, in which particles or physical objects are treated using quantum wave functions but the surrounding environment (for example a potential well
Potential well
A potential well is the region surrounding a local minimum of potential energy. Energy captured in a potential well is unable to convert to another type of energy because it is captured in the local minimum of a potential well...
or a bulk electromagnetic field
Electromagnetic field
An electromagnetic field is a physical field produced by moving electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction...
or gravitational field
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...
) is treated classically. First quantization is appropriate for studying a single quantum-mechanical system being controlled by a laboratory
Laboratory
A laboratory is a facility that provides controlled conditions in which scientific research, experiments, and measurement may be performed. The title of laboratory is also used for certain other facilities where the processes or equipment used are similar to those in scientific laboratories...
apparatus
Apparatus
Apparatus may refer to:*Technical term for body of the Soviet and post-Soviet governments *Machine*Equipment*Critical apparatus, the critical and primary source material that accompanies an edition of a text-See also:*Fire apparatus...
that is itself large enough that classical mechanics
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
is applicable to most of the apparatus.
First quantization is the subject studied in most undergraduate quantum mechanics courses, and in which the Schrodinger Equation
Schrödinger equation
The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....
and Heisenberg matrix mechanics
Matrix mechanics
Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925.Matrix mechanics was the first conceptually autonomous and logically consistent formulation of quantum mechanics. It extended the Bohr Model by describing how the quantum jumps...
(together with bra-ket notation
Bra-ket notation
Bra-ket notation is a standard notation for describing quantum states in the theory of quantum mechanics composed of angle brackets and vertical bars. It can also be used to denote abstract vectors and linear functionals in mathematics...
) are most simply applied. It may be contrasted with Second quantization, which includes quantum-mechanical uncertainty effects in all aspects of an experiment including the controlling fields and boundary conditions.