New generalized uncertainty principle from the doubly special relativity

TL;DR

This paper introduces a new generalized uncertainty principle derived from doubly special relativity, where coordinates stay unchanged at high energies but momentum is deformed and bounded, affecting quantum mechanical problems.

Contribution

It presents a novel form of GUP based on doubly special relativity, with specific implications for quantum mechanics at high energies.

Findings

Coordinate remain unaltered at high energy

Momentum is deformed and bounded from above

Quantum problems like the box and harmonic oscillator are analyzed

Abstract

Based on the doubly special relativity we find a new type of generalized uncertainty principle (GUP) where the coordinate remain 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.