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Bound states in the continuum of fractional Schr\"odinger equation in the Earth's gravitational field and their effects in the presence of a minimal length: applications to distinguish ultralight part

来源于:arXiv
In this paper, the influence of the fractional dimensions of the L\'evy path under the Earth's gravitational field is studied, and the phase transitions of energy and wave functions are obtained: the energy changes from discrete to continuous and wave functions change from non-degenerate to degenerate when dimension of L\'evy path becomes from integer to non-integer. By analyzing the phase transitions, we solve two popular problems. First, we find an exotic way to produce the bound states in the continuum (BICs), our approach only needs a simple potential, and does not depend on interactions between particles. Second, we address the continuity of the energy will become strong when the mass of the particle becomes small. By deeply analyze, it can provide a way to distinguish ultralight particles from others types in the Earth's gravitational field, and five popular particles are discussed. In addition, we obtain analytical expressions for the wave functions and energy in the Earth's gra 查看全文>>