for the potential
$$V(x)=-\frac{1}{1+\frac{x^2}{m^2}}$$
we can approximate the wave function and bounded state accurately for $x << m$ as simple harmonic oscillator, so what are we gonna do if $x$ is large compared to $m$? Is it the number of bounded state in this exact potential is no more than the bound state energy that is great than 0? How do we find the exact number?
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