Final answer:
Two wave functions are orthogonal when their inner product is zero, which is a crucial concept in quantum mechanics implying non-overlapping quantum states. This orthogonality is unrelated to their amplitudes, wavelengths, or frequencies but corresponds to the probability of finding them in the same physical situation being zero.
Step-by-step explanation:
Two wave functions i and j belonging to an operator O are said to be orthogonal wave functions if their inner product is zero. This means that the integral of the product of their wave functions over all space is zero, indicating that the probability of finding the two states in the same physical situation is nil. This orthogonality is a key concept in quantum mechanics and relates to the independence or non-overlap of quantum states.
Orthogonality does not depend on equal amplitudes, wavelengths, or frequencies. For example, during wave interference, the amplitudes of two waves get added when they are out of phase and propagating along the same line, leading to either constructive or destructive interference, depending on their relative phases. Pure destructive interference, where the waves cancel each other out completely, occurs when two waves with equal frequencies and amplitudes are perfectly out of phase while propagating along the same line.