Show directly that the trial wave function Y(x, t) = er(kx - wt) satisfies in a2p ( x , t ) + VY(x, t). ot 2m ax2 The derivatives are (Use the following as necessary: 1, k, and w.) E i(kx - cot) at -iwe X and = *2ei ( kx - cot) X Substituting in the time-dependent Schrodinger equation gives (Use the following as necessary: 'P, p and m.) 2 + VY 2m X The result is E = K+V where K is the kinetic energy, which is a statement of conservation of mechanical energy