含时量子势连续介质中的可冻结束缚态
Freezable bound states in the continuum for time-dependent quantum potentials
摘要：
本文利用超对称量子力学构造了薛定谔方程的含时势。所产生的势具有量子态的性质，即在特定的阈值时间$t_F$之后，当势不再改变时，演化态变成连续统中的束缚态，其概率分布冻结。在几何相位因子分解后，态满足一个具有与时间无关的势的定态薛定谔方程。该程序可以扩展到支持一个以上的连续束缚态。封闭表达式的潜力，在连续的束缚态，散射态的例子从自由粒子。
英文摘要：
In this work, we construct time-dependent potentials for the Schrödinger equation via supersymmetric quantum mechanics. The generated potentials have a quantum state with the property that after a particular threshold time $t_F$, when the potential does no longer change, the evolving state becomes a bound state in the continuum, its probability distribution freezes. After the factorization of a geometric phase, the state satisfies a stationary Schrödinger equation with time-independent potential. The procedure can be extended to support more than one bound state in the continuum. Closed expressions for the potential, the bound states in the continuum, and scattering states are given for the examples starting from the free particle.
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