标题： 从最小不确定性方法的角度看量子黑洞作为简谐振子 显示英文标题

标题： Quantum Black Hole as a Harmonic Oscillator from the Perspective of the Minimum Uncertainty Approach

摘要： 从施瓦茨希尔德黑洞内部的惠勒-德维特方程出发，该方程是通过以规范相空间坐标为基准的哈密顿量推导得出的，我们证明通过应用一个简单的重新参数化，这个方程可以表示为量子线性谐振子的本征值方程。 在标准量化框架下，我们发现所得波函数在经典奇点区域发散，且黑洞内部所有状态的克里斯托费尔标量的期望值未定义。 然而，当我们将最小不确定性方法应用于量化过程时，得到的波函数既明确又平方可积。 此外，这些状态的克里斯托费尔标量的期望值在整个黑洞内部保持有限，这表明在该方法中经典奇点被解决，由一个最小半径所取代。 显示英文摘要

摘要： Starting from the Wheeler-DeWitt equation for the Schwarzschild black hole interior, which is derived from a Hamiltonian formulated in terms of canonical phase space coordinates, we show that by applying a simple reparametrization, this equation can be expressed as the eigenvalue equation of a quantum linear harmonic oscillator. Within the standard quantization framework, we find that the resulting wave function diverges in the region of the classical singularity, and the expectation value of the Kretschmann scalar is undefined for all states within the black hole. However, when we apply the minimal uncertainty approach to the quantization process, we obtain a wave function that is both well-defined and square-integrable. Additionally, the expectation value of the Kretschmann scalar for these states remains finite throughout the black hole's interior, suggesting that the classical singularity is resolved in this approach, replaced it by a minimum radius.