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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.
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 mechanics, the probability current (sometimes called probability flux) is a mathematical quantity describing the flow of probability. Specifically, if one thinks of probability as a heterogeneous fluid, then the probability current is the rate of flow of this fluid.
The probability density function of the n = 30 state of the quantum harmonic oscillator. The solid plot represents the quantum mechanical probability density, while the dotted line represents the classical probability density. The dashed vertical lines indicate the classical turning points of the system.
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 .
and the probability that particle 1 is in region R 1 with spin s z1 = m 1 and particle 2 is in region R 2 with spin s z2 = m 2 etc. at time t is the integral of the probability density over these regions and evaluated at these spin numbers:
Position space probability density of a Gaussian wave packet moving in one dimension in free space. The simplest example of a quantum system with a position degree of freedom is a free particle in a single spatial dimension. A free particle is one which is not subject to external influences, so that its Hamiltonian consists only of its kinetic ...
Quantum chaos; EPR paradox; Density matrix; Scattering theory ... P = Probability that particle 1 has position r 1 in volume V 1 with spin s z1 and particle 2 has ...