Dispersion relation of matter waves in non-relativistic quantum mechanics: One-dimensional Schrodinger's equation for the "probability amplitude" (x, t) of a free particle with mass m is given as jh t = h 2 2m 2 x2 , where h denotes the Planck's constant normalized by 2 (and with j replaced by i in physics books) this equation governs the quantum mechanical model of the motion of the particle (described in a non-classical probabilistic manner). a) Determine the dispersion relation of wave-like solutions (x, t) = e j(tkx) = e i(kxt) of Schrodinger's equation by evaluating and simplifying the equation using the wave solution that is, obtain the pertinent vs k relation after replacing in the equation by e i(kxt)