Final answer:
The degeneracy of the wave solutions refers to the number of different wave functions that correspond to the same energy level. In quantum mechanics, the stationary states of a system are determined by the solutions to the Schrödinger equation.
Step-by-step explanation:
The degeneracy of the wave solutions refers to the number of different wave functions that correspond to the same energy level. In quantum mechanics, the stationary states of a system are determined by the solutions to the Schrödinger equation. Each stationary state has a unique energy level, and often multiple wave functions can have the same energy. These different wave functions are referred to as degenerate wave solutions.
An example of degeneracy can be seen in the quantum particle in a box system, where the energy levels are quantized. For each energy level, there can be multiple wave functions with different spatial profiles, but the same energy. Each of these wave functions represents a different configuration that the particle can be in while having the same energy.
It is important to note that the energy of the particle is related to the curvature of the wave function, as the question mentioned. Positive energies correspond to concave down (negative curvature) wave functions, while negative energies correspond to concave up (positive curvature) wave functions.