Spontaneous breakdown of % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBqj3BWbIqubWexLMBb50ujbqegm0B % 1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqr % Ffpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0F % irpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaa % GcbaWefv3ySLgznfgDOfdarCqr1ngBPrginfgDObYtUvgaiuaacqWF % pepucqWFtepvaaa!46A4! $$ \mathcal{P}\mathcal{T} $$ symmetry in the complex Coulomb potential
| Autor: | G. Lévai |
|---|---|
| Rok vydání: | 2009 |
| Předmět: | |
| Zdroj: | Pramana. 73:329-335 |
| ISSN: | 0973-7111 0304-4289 |
| DOI: | 10.1007/s12043-009-0125-5 |
| Popis: | The \( \mathcal{P}\mathcal{T} \) symmetry of the Coulomb potential and its solutions are studied along trajectories satisfying the \( \mathcal{P}\mathcal{T} \) symmetry requirement. It is shown that with appropriate normalization constant the general solutions can be chosen \( \mathcal{P}\mathcal{T} \) -symmetric if the L parameter that corresponds to angular momentum in the Hermitian case is real. \( \mathcal{P}\mathcal{T} \) symmetry is spontaneously broken, however, for complex L values of the form L = −1/2 + iλ. In this case the potential remains \( \mathcal{P}\mathcal{T} \) -symmetric, while the two independent solutions are transformed to each other by the \( \mathcal{P}\mathcal{T} \) operation and at the same time, the two series of discrete energy eigenvalues turn into each other’s complex conjugate. |
| Databáze: | OpenAIRE |
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