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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
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