An alternative quantum theory for single particles bounded in the external field proposed in 1986(Huang X.Y.,Phys.Lett.A.,1986,115:310)is further developed from which the energy of the state for the single particle takes one of the eigenvalues of the quantum Hamiltonian,and the usual quantum mechanics for the particle in a stationary state holds only in the statistical sense.In light of the theory,the particle of definite energy,ground-state-energy for instance,can exhibit a novel periodic behavior.This result for the ground-state-energy state neutron in the Earth's gravitational field is experimentally testable using ultracold neutron beam passing through the same apparatus that was devised in 2002 to identify the energy quantization of neutron in the field(Nesvizhevsky V.V.,et al.,Nature,2002,415:297).
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