First, Second Quantization and Q-Deformed Harmonic Oscillator

IWTCP-2; NCTP-39

Van Ngu, Man^1 ; Vinh, Ngo Gia^2 ; Lan, Nguyen Tri^3 ; Thanh, Luu Thi Kim^4 ; Viet, Nguyen Ai^3

Hung Yen Industrial Colleage, Hung Yen Province, Viet Nam^1

Bac Ninh Department of Education and Training, Bac Ninh Province, Viet Nam^2

Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan street, Ba Dinh, Hanoi, Viet Nam^3

Hanoi Pedagogical University No.2, Vinh Phuc Province, Viet Nam^4

关键词: Annihilation operators;    Commutation relation;    Coordinate representations;    Deformation parameter;    Fine structures;    Harmonic oscillators;    Momentum operators;    Second quantization;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/627/1/012021/pdf
DOI  :  10.1088/1742-6596/627/1/012021

来源: IOP

【 摘 要 】

Relations between the first, the second quantized representations and deform algebra are investigated. In the case of harmonic oscillator, the axiom of first quantization (the commutation relation between coordinate and momentum operators) and the axiom of second quantization (the commutation relation between creation and annihilation operators) are equivalent. We shown that in the case of q-deformed harmonic oscillator, a violence of the axiom of second quantization leads to a violence of the axiom of first quantization, and inverse. Using the coordinate representation, we study fine structures of the vacuum state wave function depend in the deformation parameter q. A comparison with fine structures of Cooper pair of superconductivity in the coordinate representation is also performed.