New generalized uncertainty principle from the doubly special relativity

Abstract

Based on the doubly special relativity we find a new type of generalized uncertainty principle (GUP) where the coordinate remains unaltered at the high energy while the momentum is deformed at the high energy so that it may be bounded from the above. For this GUP, we discuss some quantum mechanical problems in one dimension such as box problem, momentum wave function, and harmonic oscillator problem.