Re: [Kwant] discretised Hamiltonian

[Joseph Weston]

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>
>  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,  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,
. 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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[Kwant] discretised Hamiltonian

[kamal ghosh]

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>  is the 
positional state. Then what signifies the "bra"? I mean,