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The solid body shows the places where the electron's probability density is above a certain value (here 0.02 nm −3): this is calculated from the probability amplitude. The hue on the colored surface shows the complex phase of the wave function. In quantum mechanics, a probability amplitude is a complex number used for describing the behaviour ...
In quantum physics, the scattering amplitude is the probability amplitude of the outgoing spherical wave relative to the incoming plane wave in a stationary-state scattering process. [1] At large distances from the centrally symmetric scattering center, the plane wave is described by the wavefunction [ 2 ]
The wave function of an initially very localized free particle. In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters ψ and Ψ (lower-case and capital psi, respectively). Wave functions are complex ...
The propagator lets one find the wave function of a system, given an initial wave function and a time interval. The new wave function is given by (,) = (′, ′) (,; ′, ′) ′. If K(x, t; x′, t′) only depends on the difference x − x′, this is a convolution of the initial wave function and the propagator.
Lüders rule has historically been known as the "reduction of the wave packet" or the "collapse of the wavefunction". [17] [18] [19] The pure state | implies a probability-one prediction for any von Neumann observable that has | as an eigenvector. Introductory texts on quantum theory often express this by saying that if a quantum measurement is ...
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.
Wave functions represent quantum states, particularly when they are functions of position or of momentum. Historically, definitions of quantum states used wavefunctions before the more formal methods were developed. [4]: 268 The wave function is a complex-valued function of any complete set of commuting or compatible degrees of freedom.
The interference involves different types of mathematical functions: A classical wave is a real function representing the displacement from an equilibrium position; an optical or quantum wavefunction is a complex function. A classical wave at any point can be positive or negative; the quantum probability function is non-negative.