I am led to believe (because it is in a paper I am reading) that(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \frac{1}{H - z} \left|\phi\rangle = \frac{1}{E - z}\left|\phi\rangle[/tex]

where [tex]H[/tex] is the hamiltonian, [tex]\left|\phi\rangle[/tex] is an energy eigenstate with energy [tex]E[/tex], and [tex]z[/tex] is a complex variable.

In attempting to understand this expression, I have realized I do not know what is meant by

[tex]\frac{1}{A}\left|\phi\rangle[/tex]

for some operator [tex]A[/tex]. Is this the same thing as the inverse of A?

Thanks.

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# Operators in denominators

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