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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.
While standard quantum mechanics postulates wave function collapse to connect quantum to classical models, some extension theories propose physical processes that cause collapse. The in depth study of quantum decoherence has proposed that collapse is related to the interaction of a quantum system with its environment.
Microscopic here implies that quantum mechanics has to be used to provide an accurate description of the system. Many can be anywhere from three to infinity (in the case of a practically infinite, homogeneous or periodic system, such as a crystal), although three- and four-body systems can be treated by specific means (respectively the Faddeev and Faddeev–Yakubovsky equations) and are thus ...
The three-body problem is a special case of the n-body problem. Historically, the first specific three-body problem to receive extended study was the one involving the Earth, the Moon, and the Sun. [2] In an extended modern sense, a three-body problem is any problem in classical mechanics or quantum mechanics that models the motion of three ...
The Mott problem is an iconic challenge to quantum mechanics theory: how can the prediction of spherically symmetric wave function result in linear tracks seen in a cloud chamber. [ 1 ] : 119ff The problem was first formulated in 1927 by Albert Einstein and Max Born and solved in 1929 by Nevill Francis Mott . [ 2 ]
A quantum algorithm for solving this problem exists. This algorithm is, like the factor-finding algorithm, due to Peter Shor and both are implemented by creating a superposition through using Hadamard gates, followed by implementing f {\displaystyle f} as a quantum transform, followed finally by a quantum Fourier transform. [ 3 ]
In quantum mechanics, the measurement problem is the problem of definite outcomes: quantum systems have superpositions but quantum measurements only give one definite result. [ 1 ] [ 2 ] The wave function in quantum mechanics evolves deterministically according to the Schrödinger equation as a linear superposition of different states.
The phenomenology of quantum physics arose roughly between 1895 and 1915, and for the 10 to 15 years before the development of quantum mechanics (around 1925) physicists continued to think of quantum theory within the confines of what is now called classical physics, and in particular within the same mathematical structures.