20.2. Simple TBA system Consider the TBA equations for a relativistic system made of one massive particle and with kernel

ϕ(θ) = 1 2π

δ(θ).

a. Solve explicitly the equation for the pseudo-energy (θ) and show that it is given by (θ) = logemRcoshθ −1#.

b. Plot the scaling function c(R) = 6 π2mR 
∞
0 coshθ log(1+e−(θ))dθ
and compute its limit at R = 0.