Seemingly easy quantum question

[bon]

Homework Statement

Show that the minimum value of E(p,x) = p^2/2m + 1/2mw^2 x^2 with respect to the real numbers p,x when they are constrained to satisfy xp = 1/2 h/2pi is 1/2 h/2pi w.

Homework Equations

The Attempt at a Solution

Ok so this seems to just be a case of finding the minimum of a function of two variables.

But if we have f=f(x,y) then min is where partial f by dx i.e. fx = fy = 0

But partial E/dx = mw^2 x and partial E/dp = p/m..so where these both = 0 x=p=0! Where have i gone wrong?

Thanks

 

[graphene]

dude, use the constraint that you've mentioned.
from the constraint, get one variable in terms of the other and substitute for it in the expression for E.
E would then be a function of just one variable...