Shape Invariant Potentials in Supersymmetric Quantum Cosmology
| Autor: | Jalalzadeh, S., Rasouli, S. M. M., Moniz, P. V. |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Universe, 8, 316 (2022) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.3390/universe8060316 |
| Popis: | In this brief review, we comment on the concept of shape invariant potentials, which is an essential feature in many settings of $N=2$ supersymmetric quantum mechanics. To motivate its application within supersymmetric quantum cosmology, we present a case study to illustrate the value of this promising tool. Concretely, we take a spatially flat FRW model in the presence of a single scalar field, minimally coupled to gravity. Then, we extract the associated Schr\"odinger-Wheeler-DeWitt equation, allowing for a particular scope of factor ordering. Subsequently, we compute the corresponding supersymmetric partner Hamiltonians, $H_1$ and $H_2$. Moreover, we point out how the shape invariance property can be employed to bring a relation among several factor orderings choices for our Schr\"odinger-Wheeler-DeWitt equation. The ground state is retrieved, and the excited states easily written. Finally, the Hamiltonians, $H_1$ and $H_2$ are explicitly presented within a $N=2$ supersymmetric quantum mechanics framework. Comment: 19 pages, 3 figures, Review article, contribution to the special issue on "Quantum Cosmology" in Universe |
| Databáze: | arXiv |
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