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