连续谱体系的双波函数量子论

Double Wavefunction Theory for Continuous Spectrum Systems

当体系的schrǒdinger方程只有连续定态解时,在任一态上求任何力学量的期待值都将得到零或无穷大,本文建立了连续谱体系的双波函数量子论.发现新的量子论比通常的量子论提供了内容丰富得多的物理学.经典的单粒子力学是双波函数量子论的经典情况.在定义了单粒子体系的均匀系综和时间系综之后,我们发现通常的量子论正好描写了这两种系综,从而只得到平凡的期待值.

When the schr(o|¨)dinger equation of a system has only the solutions of continuous stationary states, either zero or infinity expectation value can be obtained for an arbitrary observable in any stationary state. In this paper, the double wavefunction theory for the continuous spectrum system is established with more abundant physical contents than the conventional quantum theory. The classical mechanics for the system is the classical limit case of this new theory. After the homogeneous and the time ensemble for a single particle system are defined, the conventional theory is found to crrectly describe these two ensembles and thus only the trivial expectation values can be obtained.