Search results
Results from the WOW.Com Content Network
The Born rule is a postulate of quantum mechanics that gives the probability that a measurement of a quantum system will yield a given result. In one commonly used application, it states that the probability density for finding a particle at a given position is proportional to the square of the amplitude of the system's wavefunction at that position.
Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms. [2]: 1.1 It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot.
Quantum mechanics is intrinsically indeterministic. The correspondence principle: in the appropriate limit, quantum theory comes to resemble classical physics and reproduces the classical predictions. The Born rule: the wave function of a system yields probabilities for the outcomes of measurements upon that system.
In consequence, quantum theory is "a tighter package than one might have first thought". [24]: 94–95 Various approaches to rederiving the quantum formalism from alternative axioms have, accordingly, employed Gleason's theorem as a key step, bridging the gap between the structure of Hilbert space and the Born rule. [c]
The definition of quantum theorists' terms, such as wave function and matrix mechanics, progressed through many stages.For instance, Erwin Schrödinger originally viewed the electron's wave function as its charge density smeared across space, but Max Born reinterpreted the absolute square value of the wave function as the electron's probability density distributed across space; [3]: 24–33 ...
Valentini's derivation of the quantum equilibrium hypothesis was criticized by Detlef Dürr and co-workers in 1992, and the derivation of the quantum equilibrium hypothesis has remained a topic of active investigation. [5] Numerical simulations demonstrate a tendency for Born rule distributions to arise spontaneously at short time scales. [6]
To predict measurement outcomes from quantum solutions, the orthodox interpretation of quantum theory postulates wave function collapse and uses the Born rule to compute the probable outcomes. [9] Despite the widespread quantitative success of these postulates scientists remain dissatisfied and have sought more detailed physical models.
In quantum mechanics, every state is described as a vector in Hilbert space. When a measurement is performed, it is convenient to describe this space using a vector basis in which every basis vector has a defined result of the measurement – e.g., a vector basis of defined momentum in case momentum is measured. The measurement operator is ...