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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]
This is often useful, and the values are characterized by the azimuthal quantum number (l) and the magnetic quantum number (m). In this case the quantum state of the system is a simultaneous eigenstate of the operators L 2 and L z, but not of L x or L y. The eigenvalues are related to l and m, as shown in the table below.
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 .
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.
In linear algebra (and its application to quantum mechanics), a raising or lowering operator (collectively known as ladder operators) is an operator that increases or decreases the eigenvalue of another operator.
These two properties means that we can apply Wick's theorem in the usual way, turning expectation values of time-ordered products of fields into products of c-number pairs, the contractions. In this generalised setting, the contraction is defined to be the difference between the time-ordered product and the normal ordered product of a pair of ...
The magnetic quantum number m is an integer satisfying −ℓ ≤ m ≤ ℓ, so for every n and ℓ there are 2ℓ + 1 different quantum states, labeled by m. Thus, the degeneracy at level n is ∑ l = … , n − 2 , n ( 2 l + 1 ) = ( n + 1 ) ( n + 2 ) 2 , {\displaystyle \sum _{l=\ldots ,n-2,n}(2l+1)={(n+1)(n+2) \over 2}\,,} where the sum ...