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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Operators in denominators

**Physics Forums | Science Articles, Homework Help, Discussion**