Solution of boundary problems in intensity-dependent nano-optics and quantum mechanics by the method of single expression

For boundary problems' solution in optics and quantum mechanics the same computational methods are in use. However, with the increase of local light intensity in nano-optics and energy of particles in quantum mechanics non-linear phenomena are appeared and, as a consequence, a new approach for boundary problems solution is topical. Non-traditional method of single expression (MSE) is an alternative approach permitting to obtain steady-state solution of boundary problems at any value of intensity-dependent non-linearity. Previously the MSE has been successfully used in wavelength-scale optics of multilayer and modulated structures. In the present work in parallel to the nano-optics the MSE's application in quantum mechanics is considered. A computer modelling of a particle interaction with the potential barrier is performed and a complete agreement with the known analytical expressions is obtained. The similarities in application of the MSE in these two areas are discussed.