Hi,
> Dear Developer, > The discretised Hamiltonan shown in Kwant release version > 1.4.0 in Article# 2.2.1 is not being understood when I try to attach > significance of "ket" and "bra" state to the symbols e.g. │i+1,j> > <i,j│etc. Such expressions are operators with non-zero matrix elements between the states |i,j> and |i+1,j>. Such operators can be used as a basis for writing down the Hamiltonian as matrix. > The discretised 1D -Hamiltonian is given like : > H= [-tΨ_n-1 -2tΨn +tΨ_n+1 ] /a^2 > "t" being hopping integral and "a' the lattice constant. To me this looks more like you're applying the Hamiltonian to a wavefunction. > In the article, │i,j> is the positional state. Then what signifies the > "bra"? I mean, <i,j│. > The question would appear very simple to understand that I know. Yet, > I am confused. > Please, help me to rightly think of the meaning of the Hamiltonian > expression. > Happy Kwanting and looking forward to fix my correct understanding. The bra is a linear functional on the space of states. Specifically, <i,j│ is a linear functional that returns the overlap of any state with the state |i,j>. This sounds like a misunderstanding of some underlying concepts; I would recommend reading a text on the foundations of quantum mechanics. Happy Kwanting, Joe
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