It is well-known that the Helmholtz equation describing scalar optics has a striking mathematical similarity with the Klein–Gordon equation of relativistic quantum mechanics. Exploiting this similarity, quantum methodologies are applied to the Helmholtz equation leading to a new formalism of scalar optics. Paraxial and aberrating Hamiltonians are derived for a general spatially varying refractive index. The beam-optical Hamiltonians thus derived give rise to wavelength-dependent contributions. Example of the graded-index medium is covered in detail. Explicit formulae relating the incident and emergent light rays for the general case of a thick lens are also presented.