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. It has been suggested that this article or section be merged with Newtonian mechanics. ... A simple introduction to this subject is provided in Basics of quantum mechanics. ... In the most restricted usage in quantum mechanics, the wavefunction associated with a particle such as an electron, is a complex-valued square integrable function ψ defined over a portion of space normalized in such a way that In Max Borns probabilistic interpretation of the wavefunction, the amplitude squared... A potential well is the region surrounding a local minimum of potential energy. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... The gravitational field is a field that causes bodies with mass to attract each other. ... Biochemistry laboratory at the University of Cologne. ... An apparatus is: A machine; or Reference tools added to a book, apart from the text, such as variant readings or translations, textual notes, a concordance, a bibliography, or an index, designed for the use of scholars studying the book. ... It has been suggested that this article or section be merged with Newtonian mechanics. ...

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. In some educational systems, an undergraduate is a post-secondary student pursuing a Bachelors degree. ... In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the time-dependence of quantum mechanical systems. ... Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg in 1925, it is also known as The Heisenberg Picture Matrix mechanics involves associating the properties of matter with matrices. ... Bra-ket notation is the standard notation for describing quantum states in the theory of quantum mechanics. ... Second quantization refers to quantizing fields by expressing them as operator-valued distributions The most elementary, or semiclassical treatments of quantum mechanics fix the number of particles and treat the field classically, including it as a parameter in the Hamiltonian or Lagrangian or whatever. ...