Spontaneous breakdown of $mathcal{PT}$ symmetry in the complex Coulomb potential

Pramana

G Lévai1¹ 

[1] Institute of Nuclear Research of the Hungarian Academy of Sciences (ATOMKI), P.O. Box 51, H-4001 Debrecen, Hungary$$

关键词: Spontaneous breakdown of $mathcal{PT}$ symmetry;    Coulomb potential;    complex energy eigenvalues.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

The $mathcal{PT}$ symmetry of the Coulomb potential and its solutions are studied along trajectories satisfying the $mathcal{PT}$ symmetry requirement. It is shown that with appropriate normalization constant the general solutions can be chosen $mathcal{PT}$ -symmetric if the 𝐿 parameter that corresponds to angular momentum in the Hermitian case is real. $mathcal{PT}$ symmetry is spontaneously broken, however, for complex 𝐿 values of the form $L = − dfrac{1}{2} + i𝜆$. In this case the potential remains $mathcal{PT}$ -symmetric, while the two independent solutions are transformed to each other by the $mathcal{PT}$ operation and at the same time, the two series of discrete energy eigenvalues turn into each other’s complex conjugate.

【 授权许可】

Unknown