TL;DR
This paper explores a one-dimensional quantum model invariant under translations and dilations, proposing a modified conformal transformation that preserves scale invariance without traditional conformal symmetry.
Contribution
It introduces a new conformal transformation that maintains scale invariance in a quantum mechanical model lacking conventional conformal symmetry.
Findings
The model is invariant under translations and dilations.
A modified conformal transformation can be defined for scale-invariant theories.
The approach broadens understanding of conformal invariance in quantum mechanics.
Abstract
We investigate a one dimensional quantum mechanical model, which is invariant under translations and dilations but does not respect the conventional conformal invariance. We describe the possibility of modifying the conventional conformal transformation such that a scale invariant theory is also invariant under this new conformal transformation.
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