Consider a particle of mass m in a one-dimensional system (coordinate x) with attractive potential energy V (x) = − A (x 2 + a 2 ) s , (1) where A > 0, a > 0 and s > 0 are positive system parameters. Use the semi-classical (Bohr-Sommerfeld) quantization rule to find out for which values of exponent s this potential would support an infinite (as opposed to finite!) number of bound states. (You do NOT need to find those bound states to answer the question!)

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Explanation.

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.