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Affine Extension of the Free-Particle--Oscillator--Inverted-Oscillator Triangle
We study the one-dimensional linear-potential system as an affine extension of the conformal triangle formed by the free particle, harmonic oscillator (HO) and inverted harmonic oscillator (IHO). Unlike these homogeneous quadratic Hamiltonians in the $sl(2,\mathbb R)$ sector, the linear-potential Ha
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