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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 ...
The Ehrenfest theorem, named after Austrian theoretical physicist Paul Ehrenfest, relates the time derivative of the expectation values of the position and momentum operators x and p to the expectation value of the force = ′ on a massive particle moving in a scalar potential (), [1]
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 ...
For an observable , the expectation value given a quantum state is A = tr ( A ρ ) . {\displaystyle \langle A\rangle =\operatorname {tr} (A\rho ).} A density operator that is a rank-1 projection is known as a pure quantum state, and all quantum states that are not pure are designated mixed .
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.
Given a guess or ansatz, the quantum processor calculates the expectation value of the system with respect to an observable, often the Hamiltonian, and a classical optimizer is used to improve the guess. The algorithm is based on the variational method of quantum mechanics.
The expectation value of the measurement can be calculated by extending from ... Quantum decoherence explains why a system interacting with an environment transitions ...
In quantum mechanics, the average, or expectation value of the position of a particle is given by = (). For the steady state particle in a box, it can be shown that the average position is always x = x c {\displaystyle \langle x\rangle =x_{c}} , regardless of the state of the particle.