(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For operator

H=f(r)γ , where γ=[itex]\bigl(\begin{smallmatrix}

0 & I\\

I& 0

\end{smallmatrix}\bigr)[/itex] , f(r) some even function.

Show that matrix element of this operator

[itex]<\psi_{a}|H|\psi_{b}>[/itex]

is non-vanishing only if ψ_a and ψ_b functions are of the opposite parity

(for example 2s and 2p1/2 functions)

3. The attempt at a solution

I can write H as

H=I H I= Ʃ H[itex]_{nm}[/itex]|psi_n><psi_m|

so the nm matrix element of H is then given as

H[itex]_{nm}[/itex] = <psi_a|H|psi_b> = <psi_a|I H I|psi_b> =<psi_a|ƩH[itex]_{nm}[/itex]|psi_n><psi_m||psi_b>

But I'm not sure how to proceed from here.

Maybe I should take a different approach. For example first to prove that operator

His an odd parity operator , then <psi_a|H|psi_b> is non-vanishing only if

psi_a and psi_b are of the opposite parity , right ?

ButHis even parity operator since f(r) is even, that is

f(-r)γ=f(r)γ , so I'm stuck again.

Can someone please clarify things form me here, how to evaluate matrix elements,

or is my conclusion that H is even wrong ?

**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!

# Homework Help: Operator matrix elements, opposite-parity functions

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