It is better for you to have studied "Feynman lectures on Physics Vol.3", because I cannot distinguish whether the words or expressions are what Feynman uses only or not and in order to summarize my questions here, I have to just quote the contents of the book.(adsbygoogle = window.adsbygoogle || []).push({});

However, one thing I notice is that "base state" that Feynman explains seems to be "basic orthonomal state vector"...

With a pair of hamiltonian matrix equation

[itex]i\hbar \frac{d{C}_{1}}{dt} = {H}_{11}{C}_{1} + {H}_{12}{C}_{2}[/itex]

[itex]i\hbar \frac{d{C}_{2}}{dt} = {H}_{21}{C}_{1} + {H}_{22}{C}_{2}[/itex]

where [itex]{C}_{x} = <x|\psi>[/itex] , [itex]\psi =[/itex] arbitrary state, the book set the states 1 and 2 as "base states". There are only two base states for some particle. Base states have a condition - [itex]<i|j> = {\delta}_{ij}[/itex].

I think the "kronecker delta" means that once the particle is in the state of j, we will not be able to find the state i, so if we suppose all the components of hamiltonian are constant, we can say [itex]{H}_{12}[/itex]and[itex]{H}_{21}[/itex] should be zero. ..............(1)

However the book says that states 1 and 2 are base states and [itex]{H}_{12}[/itex]and[itex]{H}_{21}[/itex] can be nonzero at the same time (if you have the book, refer equ. (9.2) and (9.3) and page 9-3.). There can be probability to transform from state 1 to state 2 and vice versa.....

Then, the relationship that I think like (1) between the "Kronecker delta" and the components of hamiltonian is not correct at all??

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# Base states with hamiltonian matrix equations (Feynman Lectures Vol.3 chap. 9-10)

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