Perturbatively deformed defects in Pöschl–Teller-driven scenarios for quantum mechanics

• Novel Pöschl–Teller-driven solutions for QM fluctuations are obtained.
• Zero-mode and excited states are obtained from deformed structures.
• The energy spectra for quantum fluctuations are perturbatively obtained.

Pöschl–Teller-driven solutions for quantum mechanical fluctuations are triggered off by single scalar field theories obtained through a systematic perturbative procedure for generating deformed defects. The analytical properties concerning the quantum fluctuations in one-dimension, zero-mode states, first- and second-excited states, and energy density profiles are all obtained from deformed topological and non-topological structures supported by real scalar fields. Results are firstly derived from an integrated λϕ4λϕ4 theory, with corresponding generalizations applied to starting λχ4λχ4 and sine  -Gordon theories. By focusing our calculations on structures supported by the λϕ4λϕ4 theory, the outcome of our study suggests an exact quantitative correspondence to Pöschl–Teller-driven systems. Embedded into the perturbative quantum mechanics framework, such a correspondence turns into a helpful tool for computing excited states and continuous mode solutions, as well as their associated energy spectrum, for quantum fluctuations of perturbatively deformed structures. Perturbative deformations create distinct physical scenarios in the context of exactly solvable quantum systems and may also work as an analytical support for describing novel braneworld universes embedded into a 5-dimensional gravity bulk.