期刊
出版社
ROYAL SOC
DOI: 10.1098/rspa.2019.0729
关键词
fractional uncertainty relation; Schrodinger equation; particle in a box; position-dependent mass; butadiene molecule
A new generalized uncertainty relation is constructed based on Li-Ostoja-Starzewski fractional gradient operator of order 0 < alpha <= 1 introduced recently in literature which is motivated from dimensional regularization method. The new generalized uncertainty relation leads to a new form of Schrodinger equation and emergent position-dependent mass. Special forms of position-dependent mass were studied and the problem of a particle in a box was explored. Dissimilar forms of allowed quantum energies were obtained which lead to different scenarios. We have confronted the theory with observations by evaluating the maximum wavelength obtained in the 1,3-butadiene molecule. Several features were discussed accordingly.
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