利用相干态方法,借助坐标-动量中介表象研究了处于热平衡状态下谐振子的密度矩阵.在此基础上,不必利用傅里叶变换关系,而仅仅通过选择不同的参数值,就可以获得坐标和动量表象下处于热平衡状态下的谐振子密度矩阵的表示式.另外,给出了直接求解密度矩阵的过程,发现此结果与厄米多项式密切相关,作为以上所求表示式的一个有效应用,通过比较两种方法的结果,揭示了一个全新的厄密多项式的关系式.
The density matrix of the harmonic oscillator in thermostat is calculated by virtue of the coherent states method and coordinate-momentum intermediate representation.The density matrix of the harmonic oscillator in thermostat is presented only through choosing different parameter values without making use of Fourier-transformation relations and direct calculation.Furthermore,the direct way to calculate the density matrix is also shown and the corresponding result is closely related to Hermite polynomials.As a useful application of the above conclusions,a fully new relation on Hermite polynomials can be revealed by comparing both of the above equivalent results.
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