标题： 区间上的量子力学自举：获得精确谱 显示英文标题

标题： Quantum mechanical bootstrap on the interval: obtaining the exact spectrum

摘要： 我们证明，对于一个特定的模型，量子力学的构想方法能够找到精确的结果。 我们考虑一个可解系统，其哈密顿量为$H=SZ(1-Z)S$，其中$Z$和$S$满足正则对易关系。 虽然这个模型可能看起来很不寻常，但通过使用适当的坐标变换，薛定谔方程可以转化为具有庞特-泰勒型势能的标准形式。 由于该系统定义在一个区间上，众所周知，$S$并不是自伴的。 然而，仍然可以实施构想方法，产生一组无限的正性约束。 使用某种算符顺序，能量本征值仅被限制在带状区域内。 然而，使用另一种顺序，我们发现有限数量的约束就足以精确确定低能级。 显示英文摘要

摘要： We show that for a particular model, the quantum mechanical bootstrap is capable of finding exact results. We consider a solvable system with Hamiltonian $H=SZ(1-Z)S$, where $Z$ and $S$ satisfy canonical commutation relations. While this model may appear unusual, using an appropriate coordinate transformation, the Schr\"odinger equation can be cast into a standard form with a P\"oschl-Teller-type potential. Since the system is defined on an interval, it is well-known that $S$ is not self-adjoint. Nevertheless, the bootstrap method can still be implemented, producing an infinite set of positivity constraints. Using a certain operator ordering, the energy eigenvalues are only constrained into bands. With an alternative ordering, however, we find that a finite number of constraints is sufficient to fix the low-lying energy levels exactly.