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In quantum mechanics and quantum field theory, the propagator is a function that specifies the probability amplitude for a particle to travel from one place to another in a given period of time, or to travel with a certain energy and momentum.
The path integral formulation is a description in quantum mechanics that generalizes the stationary action principle of classical mechanics.It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude.
In classical mechanics, the propagators are functions that operate on the phase space of a physical system. In quantum mechanics, the propagators are usually unitary operators on a Hilbert space. The propagators can be expressed as time-ordered exponentials of the integrated Hamiltonian. The asymptotic properties of time evolution are given by ...
This is closely tied to the functional integral formulation of quantum mechanics, also invented by Feynman—see path integral formulation. The naïve application of such calculations often produces diagrams whose amplitudes are infinite , because the short-distance particle interactions require a careful limiting procedure, to include particle ...
In physics, the fundamental solution, (Green's function), or propagator of the Hamiltonian for the quantum harmonic oscillator is called the Mehler kernel.It provides the fundamental solution [3] φ(x,t) to
In quantum mechanics, a density matrix (or density operator) is a matrix that describes an ensemble [1] of physical systems as quantum states (even if the ensemble contains only one system). It allows for the calculation of the probabilities of the outcomes of any measurements performed upon the systems of the ensemble using the Born rule .
The Källén–Lehmann spectral representation, or simply Lehmann representation, gives a general expression for the (time ordered) two-point function of an interacting quantum field theory as a sum of free propagators. It was discovered by Gunnar Källén in 1952, and independently by Harry Lehmann in 1954.
Quantum mechanics describes the nature of atomic and subatomic systems using Schrödinger's wave equation. The classical limit of quantum mechanics and many formulations of quantum scattering use wave packets formed from various solutions to this equation. Quantum wave packet profiles change while propagating; they show dispersion.