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Journal of Physics: Conference Series 627, 012021 (2015)

ISSN: 1742-6596

First, Second Quantization and Q-Deformed Harmonic Oscillator

Man Van Ngu, Ngo Gia Vinh, Nguyen Tri Lan, Luu Thi Kim Thanh and Nguyen Ai Viet

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 ne structures of Cooper pair of superconductivity in the coordinate representation is also performed.

DOI: doi:10.1088/1742-6596/627/1/012021