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In quantum physics and quantum chemistry, an avoided crossing (AC, sometimes called intended crossing, [1] non-crossing or anticrossing) is the phenomenon where two eigenvalues of a Hermitian matrix representing a quantum observable and depending on continuous real parameters cannot become equal in value ("cross") except on a manifold of dimension . [2]
The effect is named after Wilhelm Hanle, who was the first to explain the effect, in terms of classical physics, in Zeitschrift für Physik in 1924. [ 8 ] [ 9 ] Initially, the causes of the effect were controversial, and many theorists mistakenly thought it was a version of the Faraday effect .
The Landau–Zener formula is an analytic solution to the equations of motion governing the transition dynamics of a two-state quantum system, with a time-dependent Hamiltonian varying such that the energy separation of the two states is a linear function of time. The formula, giving the probability of a diabatic (not adiabatic) transition ...
In quantum field theory, a branch of theoretical physics, crossing is the property of scattering amplitudes that allows antiparticles to be interpreted as particles going backwards in time. Crossing states that the same formula that determines the S-matrix elements and scattering amplitudes for particle to scatter with and produce particle and ...
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In probability theory, Rice's formula counts the average number of times an ergodic stationary process X(t) per unit time crosses a fixed level u. [1] Adler and Taylor describe the result as "one of the most important results in the applications of smooth stochastic processes." [2] The formula is often used in engineering. [3]
The time interval may be controlled by a level crossing predictor, an electronic device which is connected to the rails of a railroad track, and activates the crossing's warning devices (lights, bells, gates, etc.) at a consistent interval prior to the arrival of a train at a level crossing. [1]
In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field. Physics is derived of formulae only.