Trajectory-coherent states for the Caldirola - Kanai Hamiltonian

Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian

Based on the technique of integration within an ordered product (IWOP) of operators we introduce the Fresnel operator for converting Caldirola-Kanai Hamiltonian into time-independent harmonic oscillator Hamiltonian. The Fresnel operator with the parameters A,B,C,D corresponds to classical optical Fresnel transformation, these parameters are the solution to a set of partial differential equations set up in the above mentioned converting process. In this way the exact wavefunction solution of the Schrödinger equation governed by the Caldirola-Kanai Hamiltonian is obtained, which represents a squ…

Squeezed States of the Generalized Minimum Uncertainty State for the Caldirola-Kanai Hamiltonian

We show that the ground state of the well-known pseudo-stationary states for the Caldirola-Kanai Hamiltonian is a generalized minimum uncertainty state, which has the minimum allowed uncertainty $Δq Δp = \hbar σ_0/2$, where $σ_0 (\geq 1)$ is a constant depending on the damping factor and natural frequency. The most general symmetric Gaussian states are obtained as the one-parameter squeezed states of the pseudo-stationary ground state. It is further shown that the coherent states of the pseudo-stationary ground state constitute another class of the generalized minimum uncertainty states.

Caldirola-Kanai Oscillator in Classical Formulation of Quantum Mechanics

The quadrature distribution for the quantum damped oscillator is introduced in the framework of the formulation of quantum mechanics based on the tomography scheme. The probability distribution for the coherent and Fock states of the damped oscillator is expressed explicitly in terms of Gaussian and Hermite polynomials, correspondingly.

Dissipative Bohmian mechanics within the Caldirola-Kanai framework: A trajectory analysis of wave-packet dynamics in viscid media

Classical viscid media are quite common in our everyday life. However, we are not used to find such media in quantum mechanics, and much less to analyze their effects on the dynamics of quantum systems. In this regard, the Caldirola-Kanai time-dependent Hamiltonian constitutes an appealing model, accounting for friction without including environmental fluctuations (as it happens, for example, with quantum Brownian motion). Here, a Bohmian analysis of the associated friction dynamics is provided in order to understand how a hypothetical, purely quantum viscid medium would act on a wave packet f…

有效Caldirola-Kanai模型用于非均匀轴向场中加速扭转狄拉克态

Effective Caldirola-Kanai Model for Accelerating Twisted Dirac States in Nonuniform Axial Fields

本文研究了在非均匀轴向场中传播的带电粒子的相对论性扭转（轨道角动量）态，通过Dirac方程和受控的无自旋近似与近轴近似，推导出横向包络满足由Caldirola-Kanai哈密顿量支配的有效非稳态Schrödinger方程，并通过Ermakov映射获得闭合形式的扭转波函数。

从Caldirola到Bateman阻尼系统的对称性之旅

A symmetry trip from Caldirola to Bateman damped systems

本文从Caldirola-Kanai阻尼谐振子出发，通过幺正扩展对称代数，自然引出Bateman对偶系统，并给出其对称群与量子化方案，实现一阶薛定谔方程。