平移和旋转对称系统中的量子力学维里定理
Quantum mechanical virial theorem in systems with translational and rotational symmetry
摘要：
以伸缩生成元G和哈密顿量H之间的交换子的形式导出了具有平移和旋转对称性的量子力学非相对论和相对论系统的广义维里定理。如果满足平移和旋转对称的条件以及定理的附加条件，则交换子[G，H]的矩阵元素在Hilbert空间的子空间上等于零。包含H，J^{2}，J_{z}和附加算子的特定交换算子集合的归一化联合特征向量形成该子空间中的正交基。预计该定理适用于大量具有平移和旋转对称性的量子力学N粒子系统。
英文摘要：
Generalized virial theorem for quantum mechanical nonrelativistic and relativistic systems with translational and rotational symmetry is derived in the form of the commutator between the generator of dilations G and the Hamiltonian H. If the conditions of translational and rotational symmetry together with the additional conditions of the theorem are satisfied, the matrix elements of the commutator [G, H] are equal to zero on the subspace of the Hilbert space. Normalized simultaneous eigenvectors of the particular set of commuting operators which contains H, J^{2}, J_{z} and additional operators form an orthonormal basis in this subspace. It is expected that the theorem is relevant for a large number of quantum mechanical N-particle systems with translational and rotational symmetry.
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