One-dimensional Harmonic Oscillator In The Coordinate Representation

As a joint-realm of information theory and statistical physics, information entropy has received a great deal of investigations. At the same time, the coordinate representation also can be exploited in calculating thermal non-classical states recently, such as coherent state. Basing on the correlative theory, and within the framework TFD, we calculate Rindler oscillator's information-entropy in the coordinate representation, and discuss the relation of its general uncertainty relationship and information-entropy, especially the relation of its thermal fluctuation and information-entropy. On the other hand, a thermal number state is defined in the coordinate representation. Then the position variance and the variance of the particle number are given in the r|-?space-time. Therefore, we draw a conclusion that the position variance of one-dimensional Minkowski oscillator is not only influenced by the temperature, but also affected by the number of particles in r\-^ spacetime.