Spontaneous breakdown of $\mathcal{PT}$ symmetry in the complex Coulomb potential
Click here to view fulltext PDF
Permanent link:
https://www.ias.ac.in/article/fulltext/pram/073/02/0329-0335
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 $L = − \dfrac{1}{2} + i\lambda$. 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.
Volume 96, 2022
All articles
Continuous Article Publishing mode
Click here for Editorial Note on CAP Mode
© 2021-2022 Indian Academy of Sciences, Bengaluru.