具有自场耦合的Schrodinger-Newton系统
The Schrodinger-Newton System with Self-Field Coupling
摘要：
我们研究了薛定谔-牛顿方程组，其中加入了引力场能量源--这种额外的非线性可以从引力理论（如广义相对论）中得到，它在这个简化的标量设置（爱因斯坦的广义相对论的前身之一）中的出现导致了自引力理论光谱的显著变化。使用迭代技术，我们比较了薛定谔-牛顿和新的，自源系统的基态能量的质量依赖性，发现它们是显着不同的。来自旧量子化的玻尔方法提供了对差异的定性描述，该差异来自自源情况中引入的附加非线性。除了比较基态能量外，我们还计算了基态和第一激发态之间的跃迁能量，比较了薛定谔-牛顿和自耦合标量情况下的发射频率。
英文摘要：
We study the Schrodinger-Newton system of equations with the addition of gravitational field energy sourcing - such additional nonlinearity is to be expected from a theory of gravity (like general relativity), and its appearance in this simplified scalar setting (one of Einstein's precursors to general relativity) leads to significant changes in the spectrum of the self-gravitating theory. Using an iterative technique, we compare the mass dependence of the ground state energies of both Schrodinger-Newton and the new, self-sourced system and find that they are dramatically different. The Bohr method approach from old quantization provides a qualitative description of the difference, which comes from the additional nonlinearity introduced in the self-sourced case. In addition to comparison of ground state energies, we calculate the transition energy between the ground state and first excited state to compare emission frequencies between Schrodinger-Newton and the self-coupled scalar case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
