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A quantum description of the surface waves in an isotropic elastic bodywithout the use of the semiclassical quantization is proposed. The problemabout the surface waves is formulated in the Lagrangian and Hamiltonianrepresentations. Within the framework of the generalized Debye model, thecontribution of the surface phonons (rayleighons) to thermodynamic functions iscalculated. It is emphasized that the role of the surface phonons can besignificant and even decisive in low-dimensional systems, granular and porousmedia, and that their contribution to the total heat capacity increases withdecreasing temperature.

Debye model for the surface phonons