Some thermodynamic features of ideal systems with nonlinear interaction

The thermodynamic properties of two two-dimensional systems are investigated comparatively. One system corresponds to a bound state of a two-dimensional harmonic oscillator, and the other corresponds to a nonlinear anharmonic oscillator. The spectrum for the harmonic oscillator is presented; for the nonlinear oscillator, the WKB spectrum and the wave functions are first calculated. The $\Omega$-potential behavior is essentially different at high temperatures. This difference may possibly be observed by investigating the temperature dependence of the heat capacity in planar anisotropic media.