Quantized space-time and its influences on some physical problems

TL;DR

This paper explores the implications of Snyder's quantized space-time on physical laws, deriving a generalized uncertainty principle, modified density of states, and analyzing the harmonic oscillator's exact solution within this framework.

Contribution

It introduces a new generalized uncertainty principle and modified density of states based on Snyder's quantized space-time, and provides an exact solution for the harmonic oscillator.

Findings

Modified density of states affects physical quantities

Derived a new generalized uncertainty principle

Solved harmonic oscillator exactly in Snyder space-time

Abstract

Based on the idea of quantized space-time of Snyder, we derive new generalized uncertainty principle and new modified density of states. Accordingly we discuss the influences of the modified density of states on some physical quantities and laws. In addition we analyzed the exact solution of the harmonic oscillator in Snyder's quantized space-time.