As a general conclusion theexamples show that it is necessary to modify the position operator.California State University, Fresno.Lee, Jaeyeong.California State University, Fresno.
This is the extension of the basic problem of finding eigenvalues in the field for a matrix or linear operator. Thus the theory works most smoothly over algebraically closed fields such as C. Sometimes, however, it is necessary to work over smaller fields and due caution is necessary. For ...
Other examples from quantum mechanics are the Liouville–von-Neumann equation for the density operator ρ(t) or master equations for dissipative systems [2]. Analytical solutions of such equations can be found only in a very limited number of cases. In most situations one must resort to ...
Bk are the Bernoulli numbers and the adjoint operator adU represents a mapping adU(V)=[U,V]=UV−VU. The k-th power of adU is understood as an iterated application of this mapping: adU0(V)=V, (3.11) adU1(V)=[U,V], (3.12) adUk(V)=adU(adUk−1(V))=[U,[U,[…,[U...
nonrelativistic quantum mechanicstime-independent Schrodinger equationmodel HamiltonianThe present work is a version of Van Vleck–Primas perturbation method in terms of generalized ladder operators. Using the superoperator approach, a fully general, self-consistent and a totally free scheme from ...
More precisely, we study an atom (an *-algebra of (quasi-local) observables for the quantum system in question, the dynamics of the system is generated by a Liouville operator acting on a positive temperature Hilbert space. Many key properties of the system, such as return to equilibrium (...
A remark on the representation of the commutator of L z and03.65Quantum theoryquantum mechanicsIn this paper the representation of the operator Lsub(z) is discussed. (C.P.)doi:10.1007/BF02748470L. C. PapaloucasSocietà Italiana di FisicaLettere al Nuovo Cimento...
Simulation of quantum systems. In order to describe the evolution of a quantum system subjected to a time-dependent potential, one must deal with the time-dependent Schrödinger equation i∂tψ(t)=H(t)ψ(t);here, H denotes the time-dependent Hamiltonian operator, and the wave function ψ...
The cases of real functions, quantum coordinate and momentum operators, time and Liouville operator, and quantum time and energy operators, are analyzed within this formalism. This procedure allows the elucidation of the properties of time in classical and quantum mechanics....
In this paper, we get the boundedness of the Calderón–Zygmund operator T on mixed-norm Herz-slice spaces, and demonstrate the necessary and sufficient conditions for the boundedness of the commutator [ b , T ] on mixed-norm Herz-slice spaces. Our results are all new when we return to ...