<p>The one-dimensional rectangular quantum well is widely employed as a basic building block for many advanced semiconductor devices. Computationally efficient routines are required to model, analyze, and optimize these devices. In this paper, we develop novel and explicit closed-form expressions to calculate the energy levels of finite symmetric and asymmetric quantum wells, aiming at compact modeling of these advanced semiconductor devices. Specifically, we propose a novel approximation method to compute the roots of trigonometric transcendental equations by means of a Taylor series expansion around a sliding expansion point. The results are fully analytical expressions that provide the eigenenergies in terms of the quantum well parameters. The obtained expressions are validated against reference numerical solutions of the transcendental equations, and an agreement greater than 99% is achieved.</p>