個爐有無人
想問下path integral formalism嘅問題
佢個idea大致係先將time evolution拆成n個/delta t嘅intervals,然後一堆數之後寫成path integral同functional integration。個phase就由個path 嘅action in出嚟
capital letters for operators.
我睇啲書個derivation,見都係話因為/delta t /to 0,所以雖然個e^iH /delta t 個H入面嘅term唔commute,例如P,Q,但係計first order 唔要second order就同commute一樣, CBH formula:
e^(i delta t (P^2+Q))=e^(idelta tP^2)e^(i delta t Q)e^(O(delta t ^2))
所以就可以拆開。之後再轉下base插下complete set咁。
個問題係,就咁睇每個e拆開之後個e^O(delta t ^2)係可以neglect,但係take delta t to 0即係n to inf,所以應個有無限多個e^()。每個error合埋晒會有e^O(delta t),所以應該唔可以neglect。唔止本書,好幾次見人都話delta t to 0,所以可以drop咗個higher order term當係commute咁做。但係加埋就唔係higher order呢
唔知我邊個位搞錯
其實仲有好多問題,不過太長,下次先