Higher-order semiclassical energy expansions for potentials with non-integer powers
In this paper, we present a semiclassical eigenenergy expansion for the potential |x|α when α is a positive rational number of the form2n/m (n is a positive integer and m is an odd positive integer). Remarkably, this expansion is found to be identical to the WKB expansion obtained for the potentialxN(N-even), if2n/m is replaced byN. Taking the limitm → 2 of the above expansion, we obtain an explicit asymptotic energy expansion of symmetric odd power potentials |x|2j+1 (j- positive integer). We then show how to develop approximate semiclassical expansions for potentials |x|α when α is any positive real number.
Volume 94, 2020
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