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如果狄拉克的《量子力学原理》有第⑤版(范洪义作)

已有 952 次阅读 2023-3-18 18:04 |系统分类:观点评述

设想如果狄拉克健在,并出他的《量子力学原理》第⑤版, 他会将Ket-bra符号的积分方法补充到他的书里吗?这个问题供读者们思考。 我这里介绍该书的初版是1930年,到1958年出第四版。对于他的符号法,狄拉克曾说:

"The symbolic method, which deals directly in an abstract way with the quantities of fundamental importance..., however, seems to go more deeply into the nature of things. It enables one to express the physical law in a neat and concise way, and will probably be increasingly used in the future as it becomes better understood and its own special mathematics gets developed."

他又说:"This work gave me more pleasure in carrying it through than any of the other papers which I have written on quantum mechanics either before or after." 

在他的晚年,又说:

"I think that is the piece of work which has most pleased me of all the works that I've done in my life....The transformation theory (became) my darling..¡- I just couldn't face giving up the transformation theory[for anything]." (Dirac, Report KFKI-1977-62, Hung. Acad. Sci.)

在 1955年,当被问到他研究物理的哲学是什么? 狄拉克在黑板上写下:‘Physical Laws should have mathematical beauty’. 我的有序算符内的积分理论有美的魅力,也许该理论会被纳入第五版吧,如果狄拉克能显灵。抑或是造物主让我降生的目的是继往开来发展狄拉克的符号法。

In the preface of

his famous book <The Principles of Quantum Mechanics>, Dirac introduced and placed great hopes on the

symbolic method: Moreover, to show his appreciation of the symbolic method, Dirac once said:

"I think that is the piece of work which has most pleased me of all the works that I've done in my life....

The transformation theory (became) my darling..¡- I just couldn't face giving up the transformation theory [for anything]." (Dirac, Report KFKI-1977-62, Hung. Acad. Sci.)

Dr. Hong-yi Fan's accomplishments not only fulfilled but also far exceeded Dirac's expectations. Dr. Fan invented the method of 'Integration Within an Ordered Product (IWOP) of operators' to fashion Dirac's symbolic method. The IWOP technique directly develops the special mathematics of symbolic method and thus makes it better understood. It strengthens and enriches Dirac's representation theory. As a result, many new operator identities for transformation theory and new useful quantum mechanical representations can be derived, of which the bipartite entangled state representation of continuum variables is the most important and fundamental.




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