Comment by antoine-levitt

Very fun! It would be interesting to do this with actual quantum mechanics (ie solving the schrodinger equation for an inverted quadratic potential). The usual bound states of the harmonic oscillator can be analytically continued into resonances with a complex energy, whose imaginary part should give the rate of decay in the situation the article discusses. Haven't checked the calculation but I would imagine this gives the same result. https://arxiv.org/abs/2012.09875 looks like it has the details.