Bound States and Quantum Chromodynamics

In classical mechanics, we talk about a particle say an electron with a position x and velocity v. In quantum mechanics, particle state is represented by complex waves \(\exp (ikx)\) or sum of such waves \(\sum _j \exp (ik_jx)\) . In complex wave \(\exp (ikx)\) , k is the wavenumber of the particle. The wave evolves in time as \(\exp (i(kx - \omega (k) t))\) , \(\omega (k)\) is the frequency of the wave and depends on wavenumber k. The dependence \(\omega (k)\) is called the dispersion relation of the wave. First postulate of quantum mechanics is that the energy of the wave is \(E = \hbar \omega (k)\) , where \(\hbar \) is a fundamental constant called Planck’s constant. Its units are angular momentum and in SI units its value is \(6.6 \times 10^{-34}\) .