Dorey, P. and Millican-Slater, A. and Tateo, R. (2005) 'Beyond the WKB approximation in PT-symmetric quantum mechanics.', Journal of physics A : mathematical and general., 38 (6). pp. 1305-1332.
The mergings of energy levels associated with the breaking of symmetry in the model of Bender and Boettcher, and in its generalization to incorporate a centrifugal term, are analysed in detail. Even though conventional WKB techniques fail, it is shown how the ODE/IM correspondence can be used to obtain a systematic approximation scheme which captures all previously observed features. Nonperturbative effects turn out to play a crucial role, governing the behaviour of almost all levels once the symmetry-breaking transition has been passed. In addition, a novel treatment of the radial Schrödinger equation is used to recover the values of local and non-local conserved charges in the related integrable quantum field theories, without any need for resummation even when the angular momentum is nonzero.
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|Publisher Web site:||http://dx.doi.org/10.1088/0305-4470/38/6/010|
|Date accepted:||No date available|
|Date deposited:||No date available|
|Date of first online publication:||February 2005|
|Date first made open access:||No date available|
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