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As a generalized uncertainty principle (GUP) leads to the effects of theminimal length of the order of the Planck scale and UV/IR mixing, somesignificant physical concepts and quantities are modified or correctedcorrespondingly. On the one hand, we derive the maximally localized states ---the physical states displaying the minimal length uncertainty associated with anew GUP proposed in our previous work. On the other hand, in the framework ofthis new GUP we calculate quantum corrections to the thermodynamic quantitiesof the Schwardzschild black hole, such as the Hawking temperature, the entropy,and the heat capacity, and give a remnant mass of the black hole at the end ofthe evaporation process. Moreover, we compare our results with that obtained inthe frameworks of several other GUPs. In particular, we observe a significantdifference between the situations with and without the consideration of theUV/IR mixing effect in the quantum corrections to the evaporation rate and thedecay time. That is, the decay time can greatly be prolonged in the formercase, which implies that the quantum correction from the UV/IR mixing effectmay give rise to a radical rather than a tiny influence to the Hawkingradiation.

Maximally localized states and quantum corrections of black hole thermodynamics in the framework of a new generalized uncertainty principle