Numerical approach to the Schroumldinger equation in momentum space

The treatment of the time-independent Schroumldinger equation in real space is an indispensable part of introductory quantum mechanics. In contrast, the Schroumldinger equation in momentum space is an integral equation that is not readily amenable to an analytical solution and is rarely taught. We present a numerical approach to the Schroumldinger equation in momentum space. After a suitable discretization process, we obtain the Hamiltonian matrix and diagonalize it numerically. By considering a few examples, we show that this approach is ideal for exploring bound states in a localized potential and complements the traditional (analytical or numerical) treatment of the Schroumldinger equation in real space.