## 1 Introduction  
The focused infrared (IR) heating method has been widely used in engineering applications because of its low cost and excellent energy efficiency; it has been used in cooking [1; 2; 3; 4], medical devices [5], drying [6; 7], and in the metal forming fields [8; 9]. IR consists of electromagnetic waves with wavelengths between 0.78 and 1000 \(\upmu\)m [2]. When IR rays reach the surface of a material, some of the IR rays are absorbed inside the material. The absorbed IR energy activates the molecules of the material, increasing the temperature of the material, as explained in [3]. This radiant heating is highly preferred in the food industry because it has a sterilizing effect as well as a heating effect [10]. An IR heater mainly consists of an IR lamp and a reflector, and various types of heating can be created according to the design of the reflector, as shown in [11]. One of the most widely used types of reflector is the elliptical-shaped reflector because it can concentrate IR energy in a very narrow area to increase the energy efficiency [10; 11]. While an elliptical reflector theoretically collects all of the IR energy emitted from the IR lamp to the target focus, diffusion reflection and shape errors distribute the IR heat flux out of the target point [12; 13]. The food industry has introduced some models to optimize the process of using IR for drying [14], baking [15; 16], roasting [17], and thawing [18]. In the modeling of food processing, more attention is paid to mass transfer due to moisture rather than IR flux distribution [10]. In the case of soldering and metal heat treatment, the IR distribution is an important issue for process optimization because there is no mass change and heating should be completed quickly [10]. [PERSON] et al. [19] and [PERSON] et al. [20] conducted optimal design and measurement of the collected energy generated by elliptical reflectors for engineering applications. [PERSON] et al. [21; 22] introduced numerical models of the IR distribution for fast heat treatment processes of metal sheets. [PERSON] et al. [23] recently conducted an optimization of the heat-assisted mechanical trimming process based on IR distribution modeling. Even though the aforementioned models have shown good results, they are mathematically complex because they are strongly affected by the complex paths of the IR rays and the geometric information of the elliptical reflector [16]. This paper presents a new approach for modeling the focused IR heating method by using quantum mechanical formulations. Even though the IR heating condition is not a pure quantum mechanical phenomenon, it is efficient to employ the superposition principle of wave functions in modeling the IR distribution [24]. The wave function can be obtained by solving the Schrodinger equation, which is a differential equation describing the quantum mechanical system. The Schrodinger equation [25] was introduced in 1926, inspired by the [PERSON]'s matter wave hypothesis [26; 27]. [PERSON] mathematically defined the wave function for a single electron-proton system of hydrogen atoms, and this equation has been commonly used in quantum mechanics. By integrating the wave functions for the spatial domain, the probability of finding particles in a specific time and space can be obtained in the quantum mechanics [28]. Because of this characteristic, the Schrodinger equation has been widely used in engineering problems that require solving probability density [29; 30; 31]. This work also uses this characteristic in the IR heating analysis. In this work, the focused IR heating condition is replaced with an infinite potential well problem of quantum mechanics. In this case, the entrance of the reflector is considered as the potential well for the IR energy, and the distributed IR energy is modeled by an energy particle having wave functions of independent eigenstates, based on the Schrodinger equation [32].