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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 ...
Quantity (common name/s) (Common) symbol/s Defining equation SI unit Dimension Wavefunction: ψ, Ψ : To solve from the Schrödinger equation: varies with situation and number of particles
The vacuum expectation value of an operator O is usually denoted by . One of the most widely used examples of an observable physical effect that results from the vacuum expectation value of an operator is the Casimir effect. This concept is important for working with correlation functions in quantum field theory. It is also important in ...
Quantum state tomography is a process by which, given a set of data representing the results of quantum measurements, a quantum state consistent with those measurement results is computed. [50] It is named by analogy with tomography , the reconstruction of three-dimensional images from slices taken through them, as in a CT scan .
Expected values can also be used to compute the variance, by means of the computational formula for the variance = [] ( []). A very important application of the expectation value is in the field of quantum mechanics.
Consider a quantum system described by the (time independent) Hamiltonian . The expectation value of a physical quantity at equilibrium temperature T {\displaystyle T} , described by the operator A ^ {\displaystyle {\hat {A}}} , can be evaluated as:
In quantum field theory, correlation functions, often referred to as correlators or Green's functions, are vacuum expectation values of time-ordered products of field operators. They are a key object of study in quantum field theory where they can be used to calculate various observables such as S-matrix elements.
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.