- #1
eljose
- 492
- 0
Legendre transform...
If we define a function f(r) with r=x,y,z,... and its Legnedre transform
g(p) with [tex] p=p_x ,p_y,p_z,... [/tex] then we would have the equality:
[tex] Df(r)=(Dg(p))^{-1} [/tex] (1) where D is a differential operator..the
problem is..what happens when g(p)=0?...(this problem is usually found in several Hamiltonians of relativity) then (1) makes no sense since a 0 matrix would have no inverse..how do you define Legendre transform then...
If we define a function f(r) with r=x,y,z,... and its Legnedre transform
g(p) with [tex] p=p_x ,p_y,p_z,... [/tex] then we would have the equality:
[tex] Df(r)=(Dg(p))^{-1} [/tex] (1) where D is a differential operator..the
problem is..what happens when g(p)=0?...(this problem is usually found in several Hamiltonians of relativity) then (1) makes no sense since a 0 matrix would have no inverse..how do you define Legendre transform then...