Minimizing E(p,x) = p²/2m + ½mω²x² with constraint xp = ℏ/2

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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
 

Discussion

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...