Quantization of Space in the Presence of a Minimal Length*Supported by National Natural Science Foundation of China under Grant Nos. 10865003 and 11464005. (1st June 2015)

• Record Type: Journal Article
• Authors: Wang, Lun-Zhou; Long, Chao-Yun; Long, Zheng-Wen
• Is Part Of: Communications in theoretical physics. Volume 63:Number 6(2015:Jun.)
• Page Start: 709
• Page End: 714
• Publication Date: 2015-06-01
• Subjects: Physics -- Periodicals; 530.105
• Languages: English
• ISSNs: 0253-6102

Abstract

<abstract> <title>Abstract</title> <p>In this article, we apply the Generalized Uncertainty Principle (GUP), which is consistent with quantum gravity theories to an elementary particle in a finite potential well, and study the quantum behavior in this system. The generalized Hamiltonian contains two additional terms, which are proportional to ap³ (the result of the maximum momentum assumption) and α²p⁴ (the result of the minimum length assumption), where α ∼ 1/M_PIc is the GUP parameter. On the basis of the work by Ali et al., we solve the generalized Schrödinger equation which is extended to include the α² correction term, and find that the length L of the finite potential well must be quantized. Then a generalization to the double-square-well potential is discussed. The result shows that all the measurable lengths especially the distance between the two potential wells are quantized in units of α₀l_PI in GUP scenario.</p> </abstract>