Salpeter-like Hamilton算子的凸性与势和
Convexity and potential sums for Salpeter-like Hamiltonians
摘要：
半相对论性哈密顿量H = β \sqrt{m^2 + p^2} + V（r），其中V（r）是R^3中的中心势，在p^2中是凹的，在p中是凸的。这一事实使我们能够得到H的离散谱的余能界。通过扩展“动能势”的概念，我们能够找到基态能量E的一般能量边界，它对应于具有形式V = sum_{i} a_{i} f^{（i）}（r）的势。在幂和对数势的情况下，其中V（r）= sum_{q\ne 0} a（q）sgn（q）r^q + a（0）ln（r），边界都可以用半经典形式E \approx \min_{r}{β\sqrt{m^2 + 1/r^2} + sum_{q\ne 0} a(q)sgn(q)(rP(q))^q + a(0)ln(rP(0))}表示。对于q =-1，1，2和对数势q = 0，提供了P数的“上限”和“下限”。一些具体的例子进行了讨论，以显示质量的界限。
英文摘要：
The semirelativistic Hamiltonian H = β\sqrt{m^2 + p^2} + V(r), where V(r) is a central potential in R^3, is concave in p^2 and convex in p. This fact enables us to obtain complementary energy bounds for the discrete spectrum of H. By extending the notion of 'kinetic potential' we are able to find general energy bounds on the ground-state energy E corresponding to potentials with the form V = sum_{i}a_{i}f^{(i)}(r). In the case of sums of powers and the log potential, where V(r) = sum_{q\ne 0} a(q) sgn(q)r^q + a(0)ln(r), the bounds can all be expressed in the semi-classical form E \approx \min_{r}{β\sqrt{m^2 + 1/r^2} + sum_{q\ne 0} a(q)sgn(q)(rP(q))^q + a(0)ln(rP(0))}. 'Upper' and 'lower' P-numbers are provided for q = -1,1,2, and for the log potential q = 0. Some specific examples are discussed, to show the quality of the bounds.
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。
