Time Dependent Schrödinger Equation

In the previous chapter we discussed some experiments which showed that particles like electrons, protons, neutrons, atoms, etc., exhibit wavelike properties. Indeed the wavelength is related to the momentum through the de Broglie relation: $$ \lambda = \frac{h}{p} $$ (1) or $$ p = \hbar k $$ (2) where k = 2π/λ and ħ = ħ/2π, h being the Planck’s constant. Thus we write $$ p = \hbar k $$ (3) where k denotes the wave vector. Further, as established by Einstein’s explanation of the photoelectric effect, the energy E of the particle is related to the frequency through the relation $$ E = \hbar \omega $$ (4)