关于二维Eschrasekhar-Coulomb哈密顿量的最大过剩电荷
On the Maximal Excess Charge of the Chandrasekhar-Coulomb Hamiltonian in Two Dimensions
摘要：
我们表明，对于二维原子或相应的磁性量子点的直接量子化相对论库仑哈密顿量，最大电子数不超过核电荷的两倍。然后将其推广到存在外磁场和原子哈密顿量的情况。这是基于$$|\bx| T(\bp) + T(\bp) |\bx| $$的正性，在两个维度上，对于非相对论性的情况$T(\bp) = \bp^2$是假的，但是在本文中对于$T(\bp) = |\bp|$被证明，即，超相对论性动能。
英文摘要：
We show that for the straightforward quantized relativistic Coulomb Hamiltonian of a two-dimensional atom -- or the corresponding magnetic quantum dot -- the maximal number of electrons does not exceed twice the nuclear charge. It result is then generalized to the presence of external magnetic fields and atomic Hamiltonians. This is based on the positivity of $$|\bx| T(\bp) + T(\bp) |\bx| $$ which -- in two dimensions -- is false for the non-relativistic case $T(\bp) = \bp^2$, but is proven in this paper for $T(\bp) = |\bp|$, i.e., the ultra-relativistic kinetic energy.
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。
