Sentence examples for position operator from inspiring English sources
where is the position operator in the representation (15).
In this section, we discuss the eigenvalue equation for the position operator and angular momentum operator.
Here we derive upper bounds for non-time averaged outside probabilities and moments of the position operator from lower bounds for transfer matrices at complex energies.
In the spin language, the different terms appearing will be nonlocal spin operators coupled linearly to the position operator of the bosons.
where the index l runs over both initial and final states, and taking into account that only the diagonal elements of the position operator survive (〈k|r|l〉=0) [18].
Given an orthonormal basis B={en} of H, we consider the time-averaged moments 〈|X|ψp〉(T) of the position operator associated to B. We derive lower bounds for the moments in terms of both spectral measure μψ and generalized eigenfunctions uψ(n,x) of the state ψ.
The lack of field operators at points appears to be analogous to the lack of position operators in QFT, which troubles the particle interpretation.
Then, we construct a new canonical pair of canonical momentum and position operators so that the pair can satisfy the Weyl relation by using the streamline coordinates.
However, for position operators there is no remedy analogous to that for field operators: while even unsharply localized particle positions do not exist in QFT (see Halvorson and Clifton 2002, theorem 2), the existence of smeared field operators demonstrates that there are at least point-like field operators.
As its application, in the Weyl relation with respect to the pair of the mv-momentum and position operators by the above new canonical pair, we find the Aharonov Bohm phase.
The eigenvalues for the position operators read begin{aligned} X_1 phi ( xi, eta ) = l_1 w( xi, eta ) phi ( xi, eta ) end{aligned} begin{aligned} X_2 phi ( xi, eta ) = l_2 w( xi, eta ) phi ( xi, eta ), end{aligned} (51 where ( w( xi, eta ) ) is a weight function.
