The authors construct explicit closed quantization contours encircling the origin for radial Schrödinger problems and use a logarithmic coordinate change to equate closed-cycle and open-connection quantization while incorporating the Maslov phase via renormalization-group arguments.
Summation of divergent series: Order-dependent mapping
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abstract
Summation methods play a very important role in quantum field theory because all perturbation series are divergent and the expansion parameter is not always small. A number of methods have been tried in this context, most notably Pade approximants, Borel--Pade summation, Borel transformation with mapping, which we briefly describe and one on which we concentrate here, Order-Dependent Mapping (ODM). We recall the basis of the method, for a class of series we give intuitive arguments to explain its convergence and illustrate its properties by several simple examples. Since the method was proposed, some rigorous convergence proofs were given. The method has also found a number of applications and we shall list a few.
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quant-ph 1years
2025 1verdicts
UNVERDICTED 1representative citing papers
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Exact WKB method for radial Schr\"odinger equation
The authors construct explicit closed quantization contours encircling the origin for radial Schrödinger problems and use a logarithmic coordinate change to equate closed-cycle and open-connection quantization while incorporating the Maslov phase via renormalization-group arguments.