Hi guys(adsbygoogle = window.adsbygoogle || []).push({});

Say I have a Hamiltonian given by

[tex]

H = \sum\limits_{i,j} {a_i^\dag H_{ij} a_j^{} }

[/tex]

I wish to perform a transformation given by

[tex]

\gamma _i = \sum\limits_j {S_{ij} a_j }.

[/tex]

Now, what my teacher did was to make the substituion [itex]\gamma_i \rightarrow a_i[/itex] and [itex]a_i \rightarrow \gamma_i[/itex], so we get the transformation

[tex]

a_i = \sum\limits_j {S_{ij} \gamma _j }.

[/tex]

This expression he then inserted inHto findHin the new basis, but I don't understand why he could just make a substituion in the transformation and then insert it? Is [itex]a_i = \sum\limits_j {S_{ij} \gamma _j }[/itex] when we express the creation/annihilation operators in terms of the transformation or what?

I hope you will shed some light on this.

Best regards,

Niles.

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# Transforming a Hamiltonian

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