论文标题
基于修改后的贝特曼拉格朗日的阻尼谐波振荡器的量化
Quantization of the damped harmonic oscillator based on a modified Bateman Lagrangian
论文作者
论文摘要
基于修改后的贝特曼·拉格朗日（MBL），开发了阻尼谐波振荡器（DHO）的量化方法；因此，阐明了DHO的一些量子机械方面。除了由MBL确定并与系统的总能量相对应的汉密尔顿操作员之外，我们还将处理DHO的能源操作员。证明DHO的能量特征值随时间呈指数减小，并且能量本征态之间的过渡是根据Schrödinger方程发生的。同样，可以指出，一个新的关键参数可以区分过渡概率的不同行为。
An approach to quantization of the damped harmonic oscillator (DHO) is developed on the basis of a modified Bateman Lagrangian (MBL); thereby some quantum mechanical aspects of the DHO are clarified. We treat the energy operator for the DHO, in addition to the Hamiltonian operator that is determined from the MBL and corresponds to the total energy of the system. It is demonstrated that the energy eigenvalues of the DHO exponentially decrease with time and that transitions between the energy eigenstates occur in accordance with the Schrödinger equation. Also, it is pointed out that a new critical parameter discriminates different behaviours of transition probabilities.
