中文摘要：

基于非对易相空间量子力学算符代数关系，通过引入阶梯算符将系统能量算符对角化，导出非对易相空间二维谐振势场中稀薄玻色气体系统的能级公式。发现激发态能级与非对易相空间参数λ有关，能级的简并度完全解除，得到稀薄玻色气体系统的内能和热容量依赖于非对易参数λ的函数关系，并讨论相空间的非对易对稀薄玻色气体内能和热容量的影响。

英文摘要：

Based on the operator algebra relation of quantum mechanics, the ladder operator is introduced to diagonalize energy operator of the system and to educe the energy level formula of the rare Bose gas in the two-dimensional harmonic oscillator potential field. It is found that the excited state level is dependent on noncommutative phase space parameter λ, and that the degeneracy of energy level is completely relieved. The functional relationship of that the internal energy and heat capoity of rare Bose gas to the noncommutative parameter λ is obtained. The effect of noncommutative phase space on the internal energy and heat capoity of rare Bose gas is also discussed.