Could you define your terms? I am assuming the < > are the standard expectation value brackets, but what are and f?
See there first few posts in this thread for LaTeX.
-Dan
Hi all,
Problem
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Show that if , then for any real function
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This is probably disgustingly simple, but it has me stumped
Sorry for the presentation, can anyone show me how to use TeX equations in my post? I am new to the forums.
Omega is an operator, (I think it is Hermitian, but I am unsure.) f is any real function, Is the expectation value for the operator Omega.Could you define your terms? I am assuming the < > are the standard expectation value brackets, but what are and f?
See there first few posts in this thread for LaTeX.
-Dan
In words - if I have understood correctly - if the complex conjugate of the result of an (hermitian) operator acting on a function is equal to minus the effect of the same (hermitian) operator acting on the complex conjugate of the same real function, then the expectation value of the (hermitian) operator is zero for any real function f.
Okay, let me try this and you can correct me if I'm wrong on any point. (This would be easier if we were to use "bra-ket" notation. If you'd like me to rewrite it, just let me know.)
is a Hermitian operator, so
is a real number, where is a wavefunction.
So we know that
From here on I am taking as a real valued function. And we know that . (Given.)
Now
<-- Since f is a real valued function
But since the expectation value is real.
Thus
Thus
-Dan
Yes, I think it would be easier in bra-ket notation. However, thanks very much, I follow your answer.
I think the main reason I was stumped is that I failed to realise that for a real function. Some, sort of mental block, I don't quite know.
Thanks again for your help.