- #1
binbagsss
- 1,254
- 11
Homework Statement
I have the criteria:
## <p'| L_{n} |p>=0 ##,for all ##n \in Z ##
##L## some operator and ## |p> ##, ## |p'> ##some different physical states
I want to show that given ## L^{+}=L_{-n} ## this criteria reduces to only needing to show that:
##L_n |p>=0 ## for ##n>0 ##
Homework Equations
look up , look down,
The Attempt at a Solution
[/B]
##<p'|L_n|p>^{+}=<p|L_n^{+}|p'>=<p|L_{-n}|p'>##
So from this I can deduce that showing :
##<p'|L_n|p>^{+}## is satisfied is equivalent to showing that ##<p|L_{-n}|p'>## is satisfied.
I.e I can reduce the criteria from showing for all ##n \in Z## to showing for ##n>0## only, BUT I am still sandwiched between two different physical states, I don't understand how this means you can reduce further to showing only that ##L_n |p>=0##, ##n >0 ## acting on solely a ket/bra...
Many thanks in advance.