Griffiths Introduction to Elementary Particles · Problem 5.20

The Feynman Calculus — David J. Griffiths

Physics — QFT · linear-potential-energy-levels

Problem

On dimensional grounds, show that the energy levels of a purely linear potential,

V(r) = F_0 r

, must be of the form

E_n = \left(\frac{(F_0 \hbar)^2}{m}\right)^{1/3} a_n

where

a_n

is a dimensionless numerical factor.