The paper deals with the Caldirola–Kanai Hamiltonian in which the potential energy is defined as a linear function of the position variable. The exact solution of the Schrödinger equation using this Hamiltonian is presented. It is shown that this solution can be utilized in the theory of electric conduction of metals and semiconductors. The main idea of this paper is that if the Caldirola–Kanai Hamiltonian is applied to conduction electrons, it is possible to calculate successfully the drift velocity of the electrons in a constant electric field. The alternative calculation of the drift velocity in the framework of the density-matrix theory which is also presented leads to the same result. A useful lesson is drawn: if the friction coefficient, the parameter defining the Caldirola–Kanai Hamiltonian, concerns the conduction electrons, it is precisely equal to the reciprocal value of the relaxation time used in the kinetic theory of the electron transport in solids.

该论文涉及 Caldirola-Kanai 哈密顿量，其中势能被定义为位置变量的线性函数。给出了使用这个哈密顿量的薛定谔方程的精确解。结果表明，该解决方案可用于金属和半导体的导电理论。本文的主要思想是，如果将 Caldirola-Kanai 哈密顿量应用于传导电子，就可以成功地计算出电子在恒定电场中的漂移速度。密度矩阵理论框架中的漂移速度的替代计算也给出了相同的结果。得出了一个有用的教训：如果摩擦系数，定义 Caldirola-Kanai 哈密顿量的参数，涉及传导电子，它恰好等于固体中电子传输动力学理论中使用的弛豫时间的倒数。