On essential self-adjointness of the relativistic hamiltonian of a spinless particle in a negative scalar potential
On essential self-adjointness of the relativistic hamiltonian of a spinless particle in a negative scalar potential
复制标题
负标量势中无自旋粒子的相对论哈密顿量的本质自伴性
DOI：
--
复制
发表时间：
1994
期刊：
影响因子：
--
通讯作者：
W. Ichinose
中科院分区：
文献类型：
--
作者：
W. Ichinose
考虑描述电磁场中无自旋粒子的相对论量子哈密顿量H，其中H与经典哈密顿量c {m 0 2 c 2 + |p−a (x)| 2相关联；1/2 + V (x)通过Weyl对应。我们证明了如果V (x)被一个多项式有界，则H在c0∞(rn)上本质上是自伴随的。这一结果与非相对论性哈密顿算子即薛定谔算子的结果有很大的不同，而与狄拉克方程的结果接近。我们的证明是用[6]中的对易子定理完成的
The relativistic quantum hamiltonian H describing a spinless particle in an electromagnetic field is considered, where H is associated with the classical hamiltonian c {m 0 2 c 2 + |p − A (x)| 2 ; 1/2 + V (x) via the Weyl correspondence. We show that if V (x) is bounded below by a polynomial, H is essentially self-adjoint on C 0 ∞ (R n ). This result is quite different from that on the non-relativistic hamiltonian, i. e. the Schrodinger operator, and is close to that on the Dirac equation. Our proof is done by using the commutator theorem in [6]