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arXiv · 2206.00083

Shape Invariant Potentials in Supersymmetric Quantum Cosmology

S. Jalalzadeh·S. M. M. Rasouli·P. V. Moniz
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Abstract

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.

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S. Jalalzadeh, S. M. M. Rasouli, P. V. Moniz. 2022-05-31. Shape Invariant Potentials in Supersymmetric Quantum Cosmology. https://doi.org/10.3390/universe8060316

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