Hi everyone, I was hoping that someone might be able to tell me if what I'm doing is legit.(adsbygoogle = window.adsbygoogle || []).push({});

Firstly, I start by saying that a unitary transform can be made between two sets of operators (this is defined in this specific way);

b[itex]_{n}[/itex] = [itex]\Sigma_{m}[/itex] U[itex]_{mn}[/itex]a[itex]_{m}[/itex] (1)

Now this is the bit I'm not sure about, if i want to do the inverse to solve for a[itex]_{m}[/itex] is the following acceptable;

[itex]\Sigma_{n}[/itex]U[itex]_{nm}[/itex]^{dagger}b[itex]_{n}[/itex] = [itex]\Sigma_{n}[/itex][itex]\Sigma_{m}[/itex]U[itex]_{mn}[/itex]U[itex]_{nm}[/itex]^{dagger}a[itex]_{m}[/itex]

Where [itex]\Sigma_{n}[/itex][itex]\Sigma_{m}[/itex]U[itex]_{mn}[/itex]U[itex]_{nm}[/itex]^{dagger} = (UU^{dagger})[itex]_{nn}[/itex]= [itex]\delta_{nn}[/itex] = 1

Thanks in advance.

If this is entirely wrong, some pointers on how I isolate a[itex]_{m}[/itex] would be appreciated.

In essence what I'm asking is given (1), what is the inverse transformation of it?

Extra information: The components of U[itex]_{mn}[/itex] are real.

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# Unitary operators

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