We explore how to apply perturbation theory to complicated time-dependent Hamiltonian systems that involve complex potentials. To do this, we introduce a generalized time-dependent oscillator to which the complex potentials are connected through a weak coupling strength. We regard the complex potentials in the Hamiltonian as the perturbed terms. Quantum characteristics of the system, such as wave functions and expectation values of the Hamiltonian, are investigated on the basis of the perturbation theory. We apply our theory to particular systems with explicit choices of time-dependent parameters. Through such applications, the time behavior of the quantum wave packets and the spectrum of expectation values of the Hamiltonian are analyzed in detail. We confirm that the imaginary parts of expectation values of the Hamiltonian are not zero but very small, whereas the real parts deviate slightly from those of the unperturbed system.

我们探索如何将扰动理论应用于涉及复杂电势的复杂时变哈密顿系统。为此，我们引入了广义时变振荡器，其复势通过弱耦合强度连接到其上。我们将哈密顿量中的复杂潜能视为扰动项。基于微扰理论研究了系统的量子特性，例如波函数和哈密顿量的期望值。我们将我们的理论应用于具有明确的时变参数选择的特定系统。通过这样的应用，详细分析了量子波包的时间行为和哈密顿量的期望值的频谱。