半相对论性N玻色子系统的Binding energies
Binding energies of semirelativistic N-boson systems
摘要：
本文导出了由半相对论哈密顿量H= \sum_{i=1}^N \sqrt（p_i^2+m^2）+ \sum_{1=i<j}^N V（r_{ij}）控制的N玻色子系统的一般解析能量界，其中V（r）是一个静态吸引对势.构造了一个双变量模型哈密顿量H_c。我们推测，<H>\ge<H_c>一般，我们证明了这对于N=3，当m=0时，N=4。这个猜想对于谐振子和非相对论性的大m极限也是有效的。这个公式允许减少缩放3-或4-体问题，其光谱底部提供能量下限。以超相对论性线性势为例，详细研究了其上、下限公式，并与已有的上、下限公式进行了比较。
英文摘要：
General analytic energy bounds are derived for N-boson systems governed by semirelativistic Hamiltonians of the form H=\sum_{i=1}^N \sqrt(p_i^2+m^2) + \sum_{1=i<j}^N V(r_{ij}), where V(r) is a static attractive pair potential. A translation-invariant model Hamiltonian H_c is constructed. We conjecture that <H> \ge <H_c> generally, and we prove this for N=3, and for N=4 when m=0. The conjecture is also valid generally for the harmonic oscillator and in the nonrelativistic large-m limit. This formulation allows reductions to scaled 3- or 4-body problems, whose spectral bottoms provide energy lower bounds. The example of the ultrarelativistic linear potential is studied in detail and explicit upper- and lower-bound formulas are derived and compared with earlier bounds.
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