Effects of elliptic oblateness on harmonic oscillator in elliptic paraboloid potential

The harmonic oscillator is an important and typical physical model in quantum mechanics and quantum optics. It is very important and widely used and has been confirmed by the development and application of science and technology. The harmonic oscillator in the elliptic paraboloid potential is studied and effects of the elliptic oblateness on the harmonic oscillator in the elliptic paraboloid potential are revealed. The energy of the harmonic oscillator in the elliptical paraboloid potential is quantized, which is described by two quantum numbers n, and m. Generally speaking, the maximum value of the probability density peak decreases as the extremum number of the probability density increases. However, this reduction is with oscillations and fluctuations, which shows even a maximum structure for the smaller quantum number. For the elliptic paraboloid potential, the spatial distribution of the probability density on different cutting surfaces is various. The flatter the ellipse is, the greater the probability density of the ellipse center, and the smaller the extreme of the edge peak of the probability density will be.