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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.
In quantum mechanics, each physical system is associated with a Hilbert space, each element of which represents a possible state of the physical system.The approach codified by John von Neumann represents a measurement upon a physical system by a self-adjoint operator on that Hilbert space termed an "observable".
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 probability of any outcome of a measurement upon a quantum system must be a real number between 0 and 1 inclusive, and in order to be consistent, for any individual measurement the probabilities of the different possible outcomes must add up to 1.
In quantum mechanics, the expectation value is the probabilistic expected value of the result (measurement) of an experiment. It can be thought of as an average of all the possible outcomes of a measurement as weighted by their likelihood, and as such it is not the most probable value of a measurement; indeed the expectation value may have zero probability of occurring (e.g. measurements which ...
Quantum tomography is a process by which, given a set of data representing the results of quantum measurements, a density matrix consistent with those measurement results is computed. [ 25 ] [ 26 ] When analyzing a system with many electrons, such as an atom or molecule , an imperfect but useful first approximation is to treat the electrons as ...
The concept of probability current is also used outside of quantum mechanics, when dealing with probability density functions that change over time, for instance in Brownian motion and the Fokker–Planck equation. [1] The relativistic equivalent of the probability current is known as the probability four-current.
Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms. [2]: 1.1 It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot.