论文标题
时间依赖时间的复合物对称势井的精确溶液
Exact solutions for time-dependent complex symmetric potential well
论文作者
论文摘要
使用伪不变的运算符方法，我们研究了在复杂的时间依赖时间依赖的质量质量的粒子模型中，$ v \ left（x，t \ right）=如果\ left（t \ prirt）\ welet \ welet x \ evert x \ vert x \ per right \ vert $。该问题是可以解决的，并且根据通风函数给出了Schrödinger波函数的分析表达。确实，有了适当的选择时间依赖性度量运算符和统一转换，对于每个区域，两个相应的伪 - 富米不变式变成了众所周知的独立于时间独立的遗产不变式，这是限制在对称线性电位孔中的粒子的汉密尔顿人的汉密尔顿。最后一个不变的特征功能是通风函数。然后，对于两个区域而言，获得的阶段是真实的，并且推导了问题的一般解决方案。
Using the pseudo-invariant operator method, we investigate the model of a particle with a time-dependent mass in a complex time-dependent symmetric potential well $V\left( x,t\right) =if\left(t\right) \left\vert x\right\vert$. The problem is exactly solvable and the analytic expressions of the Schrödinger wavefunctions are given in terms of the Airy function. Indeed, with an appropriate choice of the time-dependent metric operators and the unitary transformations, for each region, the two corresponding pseudo-Hermitian invariants transform into a well-known time-independent Hermitian invariant which is the Hamiltonian of a particle confined in a symmetric linear potential well. The eigenfunctions of the last invariant are the Airy functions. Then, the phases obtained are real for both regions and the general solution to the problem is deduced.
