What's the difference between them

[enricfemi]

<n|m> ;


|m><n| ;

 

[pam]

<n|m> is a number.
|m><n| is an operator that would act on one wave function to give a different one.

 

[enricfemi]

appreciate it!

i know the product.
but what the operator is?
is it pesi(m)pesi(n)*?

 

[enricfemi]

do you mean :
when it act on one wave function,it denotes
|m><n|a> ?

 

[Gerenuk]

Think of it as *all* 1xN matrices
<br /> |n&gt;=A=\begin{pmatrix}<br /> a\\b\\c\\\ldots<br /> \end{pmatrix}<br />
<br /> &lt;n|=A^\dag=\begin{pmatrix}<br /> a^* &amp; b^* &amp; c^* &amp; \ldots<br /> \end{pmatrix}<br />
<br /> \psi_n(x)=&lt;x|n&gt;<br />
Then you see that |m&gt;&lt;n| is a matrix ("sort of operator"). &lt;m|n&gt; is a number (like the vector scalar product). Note that &lt;n|m&gt;\neq \psi_n^*(x)\psi_m(x), however since \sum_x |x&gt;&lt;x|=1
&lt;n|m&gt;=\sum_x &lt;n|x&gt;&lt;x|m&gt;=\sum_x \psi_n^*(x)\psi_m(x)
So
1. don't rearrange |n> expressions
2. only numbers <n|m> commute
3. if you ever get to <x|n>, you can substitute with \psi_n(x)

 

[Meir Achuz]

do you mean :
when it act on one wave function,it denotes
|m><n|a> ?

Yes...