论文标题
粒子跌落到奇异电位的中心：经典与量子精确溶液
Fall of a Particle to the Center of a Singular Potential: Classical vs. Quantum Exact Solutions
论文作者
论文摘要
在经典和量子案例中描述了粒子落到非规范奇异电位的中心的精确溶液并进行比较。我们在常规Schrödinger's方程的帮助下检查量子问题。在秋季，波函数空间定位区域合同分为一个零维点。对于秋季吸引力的潜力，哈密顿量是非热的。因此，波函数规范发生时间依赖性。它要求对这种连续性方程式的延伸和平均值计算规则进行扩展。令人惊讶的是，量子和古典解决方案表现出惊人的相似性。特别是，在粒子能量等于零，两者都是自相似的。量子和经典自相似解决方案的特征空间尺度遵守相同的时间依赖性。我们提出了表明这些自相似解决方案的参数是吸引更广泛的解决方案的吸引者，描述了粒子有限能量的下降。
Exact solutions describing a fall of a particle to the center of a non-regularized singular potential in classical and quantum cases are obtained and compared. We inspect the quantum problem with the help of the conventional Schrödinger's equation. During the fall, the wave function spatial localization area contracts into a single zero-dimensional point. For the fall-admitting potentials, the Hamiltonian is non-Hermitian. Because of that, the wave function norm occurs time-dependent. It demands an extension to this case of the continuity equation and rules for mean value calculations. Surprisingly, the quantum and classical solutions exhibit striking similarities. In particular, both are self-similar at the particle energy equals zero. The characteristic spatial scales of the quantum and classical self-similar solutions obey the same temporal dependence. We present arguments indicating that these self-similar solutions are attractors to a broader class of solutions, describing the fall at finite energy of the particle.
