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Normally, the half-harmonic oscillator is active when $x>0$ and absent when$x<0$. From a canonical quantization perspective, this leads to oddeigenfunctions being present while even eigenfunctions are absent. In thatcase, only the usual odd eigenfunctions will appear if the wall slides tonegative infinity. However, if an affine quantization is used, sliding the wallaway shows that all the odd and even eigenfunctions are encountered, exactlylike any full-harmonic oscillator. We provide numerical support for this.

Proof that Half-Harmonic Oscillators become Full-Harmonic Oscillators after the "Wall Slides Away"