- #1
wormhole
- 29
- 0
how do i find minimum for this potential:
u(r)=L^2/2*m*r^2 - b*exp(-ar)/r ?
b,a - constants
L - angular momentum
m - mass
u`(r)=L^2/m+b*exp(-ar)*r(a*r-1)
(u`(r*):=0 => r*=r*(a,b,L,m) )
i plotted the function for some values of b,a,L and m and i see that for certain values there is a minimum but i just can't figure out how do i find the right r.
can anyone help/give some hint?
u(r)=L^2/2*m*r^2 - b*exp(-ar)/r ?
b,a - constants
L - angular momentum
m - mass
u`(r)=L^2/m+b*exp(-ar)*r(a*r-1)
(u`(r*):=0 => r*=r*(a,b,L,m) )
i plotted the function for some values of b,a,L and m and i see that for certain values there is a minimum but i just can't figure out how do i find the right r.
can anyone help/give some hint?