In this study, we introduce and investigate a family of quantum mechanical models in 0 + 1 dimensions, known as generalized Born quantum oscillators. These models represent a one-parameter deformation of a specific system obtained by reducing the Nambu-Goto theory to 0 + 1 dimensions. Despite these systems showing significant similarities with TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ extrm{T}\\overline{\ extrm{T}} $$\\end{document}-type perturbations of two-dimensional relativistic models, our analysis reveals their potential as interesting regularizations of the Berry-Keating theory. We quantize these models using the Weyl quantization scheme up to very high orders in ħ. By examining a specific scaling limit, we observe an intriguing connection between the generalized Born quantum oscillators and the Riemann-Siegel θ function.