We present the Galerkin spectral method as a tool for the quantization of hamiltonian systems. This method can be introduced as a topic in an undergraduate introductory Physics course on Quantum Mechanics. Compared to the finite differences method, the spectral method allows greater precision, in addition to providing analytical expressions for the energy eigenfunctions, as well as being sufficiently simple to be exposed in about four hours. In the present work, we present the method in detail, applying it to the Schrödinger equation for the simple harmonic oscillator and for the quartic oscillator. The precision of results is compared to those yielded by the method of finite differences.
Keywords:
Hamiltonian systems; Schrödinger equation; Galerkin's spectral method
