BornRegel

BornRegel is a term that may be used to refer to the Born rule in quantum mechanics. In many contexts, the standard English name is the Born rule, while in German it is written as Born-Regel or Bornregel. The concatenated form BornRegel is uncommon and can appear in informal contexts, software names, or as a stylized designation in some publications.

The Born rule provides the link between the mathematical description of a quantum system and experimental outcomes. Formally, if a system is described by a wavefunction ψ and a measurement has eigenstates |φi⟩, the probability of obtaining the i-th outcome is P(i) = |⟨φi|ψ⟩|^2. In position space, the probability density for finding a particle at position x is P(x) = |ψ(x)|^2. The rule is a foundational postulate of quantum mechanics and is essential for making statistical predictions about measurements.

Origins and interpretation: The rule was introduced by Max Born in the early 20th century and has been repeatedly validated by experiments. It is interpreted in various ways depending on the philosophical stance toward quantum mechanics, with dominant views including the Copenhagen interpretation and many-worlds interpretation. While the mathematical form is universally accepted, questions about the meaning of probability and measurement persist in foundational discussions.

See also: Quantum mechanics, Wavefunction, Measurement problem, Probability interpretation.