标题： 无自旋薛尔珀特方程：能量级的拉盖尔界 显示英文标题

标题： Spinless Salpeter Equation: Laguerre Bounds on Energy Levels

摘要： 无自旋的Salpeter方程可以被视为对Bethe-Salpeter形式主义的标准近似，旨在描述相对论量子场理论中的束缚态，或者作为对常规非相对论Schrödinger形式主义的一种在某种程度上相对论的简化推广。 由于相应哈密顿量中存在相对论动能的平方根算符，这种算符较难处理，因此对应（离散）能级谱通常无法解析地确定。 因此，我们展示如何通过在解的空间希尔伯特空间中选择一些巧妙的基向量，至少对相当大一类幂律势能，可以计算出这些能级的上界（有时甚至非常精确），对于最低能级甚至可以解析地计算。 显示英文摘要

摘要： The spinless Salpeter equation may be considered either as a standard approximation to the Bethe--Salpeter formalism, designed for the description of bound states within a relativistic quantum field theory, or as the most simple, to a certain extent relativistic generalization of the costumary nonrelativistic Schr\"odinger formalism. Because of the presence of the rather difficult-to-handle square-root operator of the relativistic kinetic energy in the corresponding Hamiltonian, very frequently the corresponding (discrete) spectrum of energy eigenvalues cannot be determined analytically. Therefore, we show how to calculate, by some clever choice of basis vectors in the Hilbert space of solutions, for the rather large class of power-law potentials, at least (sometimes excellent!) upper bounds on these energy eigenvalues, for the lowest-lying levels this even analytically.