ON THE ADIABATIC THEOREM OF QUANTUM MECHANICS
ON THE ADIABATIC THEOREM OF QUANTUM MECHANICS
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DOI：
10.1143/jpsj.5.435
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发表时间：
1950-01-01
影响因子：
1.7
通讯作者：
KATO, T
中科院分区：
文献类型：
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作者：
KATO, T
‘U4，d GB：T_i-Hlibt(1)’一般没有稳定解(我们把普朗克常数h设为锌)。但在H_i变化非常慢的极限下，当系统从fi‘的定态启动时，会经过相应的定态。这是量子力学绝热定理的断言；到目前为止，对绝热定理最完整的证明是由于Born和FockflL(以下引用为BF)。他们的证明就特征值交叉的发生而言是非常普遍的，但在其他方面，它仍然受限于两个基本假设：H的谱由-纯离散特征值组成；-ii)这些特征值是非退化的，除非交叉引起偶然退化。他们的论点不能推广到更一般的情况，因为他们在fi中同时考虑了(1)对应于离散特征函数的完备系统的解的个数；从物理的观点来看，这些结论是相当随机的，因为(1)对应于H的某一特定本征值/1的解本质上是受远离1的那些光谱部分的性质、离散的或连续的等所利用的(1)的解是不可信的。在本说明中，我们将给出一个新的
‘U4,'d£: T_i-Hlibt (1)'has in general no stationary solution (we put the Planck constant h equal to Zn). But in the limit when the change of H, is made infinitely slow, the system, when started from a stationary state of HO’, passes through the corresponding stationary. states of H, for all t. This is the assertion of the adiabatic theorem of quantum mechanics; The most complete proof hitherto given to the adiabatic theorem is due to Born and Fockfll-(hereafter quoted as BF). Their proof is very general so far as concerns the occurrence of crossing of eigenvalues, but in other respects it is still restricted two essential assumptions: it the spectrum of H, consists of-purely discrete eigenvalues;-ii) these eigenvalues are non-degenerate except for accidental degeneracy caused by crossing.‘Their argument cannot be extended to more general case without radical modification, for they consider simultaneously infinite number of solu-tions of (1) corresponding to the complete system of discrete eigenfunctions; which does not exist in general case.From thephysical point of view, these as-sumptions i), ii) are rather artificial, for it is not plausible that the solution of (1) corresponding to some particular eigenvalue/1, of H, should be influenced essentially by the nature, discrete or continuous etc., of those parts of the spectrum which are distant from 1,. In the present note we shall give a new