论文标题
旋转器的代数和相对论氢原子
Algebra of the spinor invariants and the relativistic hydrogen atom
论文作者
论文摘要
结果表明，可以使用狄拉克方程的三个旋转器的代数来求解具有库仑电势的狄拉克方程，而无需涉及超对称量子力学的方法。关于旋转转换，狄拉克·哈密顿（Dirac Hamiltonian）是不变的，这表明dirac方程的动态（隐藏）对称性$ su（2）$。狄拉克方程的总对称是对称$ SO（3）\ otimes su（2）$。 $ SO（3）$对称组的生成器由总动量操作员给出，$ SU（2）$组的发电机是由Dirac，Johnson-Lippmann和New Spinor Inforniants在Spinor Space中的矢量旋转给出的。结果表明，使用代数方法解决狄拉克问题，人们可以计算相对论氢原子的特征态和特征力，并揭示主量子数作为独立数的基本作用，即使它表示为其他量子数的组合。
It is shown that the Dirac equation with the Coulomb potential can be solved using the algebra of the three spinor invariants of the Dirac equation without the involvement of the methods of supersymmetric quantum mechanics. The Dirac Hamiltonian is invariant with respect to the rotation transformation, which indicates the dynamical (hidden) symmetry $ SU(2) $ of the Dirac equation. The total symmetry of the Dirac equation is the symmetry $ SO(3) \otimes SU(2) $. The generator of the $ SO(3) $ symmetry group is given by the total momentum operator, and the generator of $ SU(2) $ group is given by the rotation of the vector-states in the spinor space, determined by the Dirac, Johnson-Lippmann, and the new spinor invariants. It is shown that using algebraic approach to the Dirac problem allows one to calculate the eigenstates and eigenenergies of the relativistic hydrogen atom and reveals the fundamental role of the principal quantum number as an independent number, even though it is represented as the combination of other quantum numbers.
