Final answer:
The student's question relates to wave functions in physics, involving superposition and characteristics of sinusoidal waves, but lacks specific details for a precise answer.
Step-by-step explanation:
The student is dealing with a physics problem related to wave functions and superposition principles in the context of quantum mechanics and optics. The specific topics include the intensity of diffraction patterns, the characteristics of sinusoidal waves, the calculations involving superposition of wave functions, and the finding of characteristic values and functions for integral equations related to these wave functions.
As a tutor, the usual approach would involve guiding the student through the mathematical process of solving such equations and providing physical interpretations of the solutions obtained. However, since the request does not contain specific, coherent details or equations that can be addressed, it is not possible to provide a step-by-step explanation or a clear answer to this query.