相关论文: Quantum Energy Expectation in Periodic Time-Depend…

Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results…

The concept of energy-dependent forces in quantum mechanics is re-analysed. We suggest a simplification of their study via the representation of each self-adjoint and energy-dependent Hamiltonian H=H(E) with real spectrum by an auxiliary…

The classical Hamiltonian system of time-dependent harmonic oscillator driven by the arbitrary external time-dependent force is considered. Exact analytical solution of the corresponding equations of motion is constructed in the framework…

At the moment, the most efficient method to compute the state of a periodically driven quantum system is using Floquet theory and the Floquet eigenbasis. The wide application of this basis set method is limited by: a lack of unique ordering…

Hamiltonian operators are gauge dependent. For overcome this difficulty we reexamined the effect of a gauge transformation on Schr\"odinger and Dirac equations. We show that the gauge invariance of the operator…

The definition of the Hamiltonian operator H for a general wave equa-tion in a general spacetime is discussed. We recall that H depends on the coordinate system merely through the corresponding reference frame. When the wave equation…

The classical and quantum dynamics in a high frequency field are found to be described by an effective time independent Hamiltonian. It is calculated in a systematic expansion in the inverse of the frequency ($\omega$) to order…

The one-dimensional time-independent Green's function $G_0$ of a quantum simple harmonic oscillator system ($V_0(x)=m \omega^2 x^2/2$) can be obtained by solving the equation directly. It has a compact expression, which gives correct…

In this work we intend to study a class of time-dependent quantum systems with non-Hermitian Hamiltonians, particularly those whose Hermitian counterpart are important for the comprehension of posed problems in quantum optics and quantum…

We present the results of a detailed analysis of a general, unstructured adiabatic quantum search of a data base of $N$ items. In particular we examine the effects on the computation time of adding energy to the system. We find that by…

We derive a generalization of Ehrenfest theorem valid for open quantum systems. From this result, we identify three contributions to the evolution of expected values: i) the explicit time dependence of the observable, ii) the…

We define a new quantum Hermitian operator (namely, the energy variance operator) which is simply duplicated from the statistical definition of energy variance in classical physics. Its expectation value yields the standard deviation of the…

The main motivation of this article is to derive sufficient conditions for dynamical stability of periodically driven quantum systems described by a Hamiltonian H(t), i.e., conditions under which it holds sup_{t in R} | (psi(t),H(t) psi(t))…

We study the conservation of energy, or lack thereof, when measurements are performed in quantum mechanics. The expectation value of the Hamiltonian of a system can clearly change when wave functions collapse in accordance with the standard…

One-particle energy eigenfunctions are used to obtain quantum averages in many particle systems. These are based on the effective local field due to fixed neighbors in classical phase space, while the averages account for the…

We derive expressions for the expectation values of the local energy and the local power transferred by an external electrical field to a many-particle system of interacting spinless electrons. In analogy with the definition of the (local)…

An algorithm is presented to calculate the electronic local time-dependent Green's operator for manganites-related hamiltonians. This algorithm is proved to scale with the number of states $N$ in the Hilbert-space to the 1.55 power, is able…

We propose a time-dependent approach to investigate the motion of electrons in quantum pump device configurations. The occupied one-particle states are propagated in real time and used to calculate the local electron density and current. An…

We consider several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schroedinger equation with variable quadratic Hamiltonians. The Green…

A new class of time-energy uncertainty relations is directly derived from the Schr\"odinger equations for time-dependent Hamiltonians. Only the initial states and the Hamiltonians, but neither the instantaneous eigenstates nor the full…