In the context of quantum mechanics, the term "boundary value" is not commonly used. However, there are some related concepts that might be relevant.
Energy Eigenvalues: In quantum mechanics, energy levels of a quantum system are often quantized, meaning they can only take certain discrete values. These allowed values are known as energy eigenvalues. The lowest energy eigenvalue is often referred to as the ground state energy, while higher energy eigenvalues correspond to excited states.
Energy Spectrum: The energy eigenvalues of a quantum system collectively form its energy spectrum. The energy spectrum provides information about the possible energies that the system can possess.
Energy Boundaries: One could refer to the highest and lowest energy eigenvalues of a quantum system as the energy boundaries. The lowest energy eigenvalue represents the lowest possible energy that the system can have (the ground state), while the highest energy eigenvalue represents the upper limit of the system's energy within a given framework.
It's important to note that the specific energy boundaries of a quantum system depend on its particular characteristics, such as the potential it is subjected to, the presence of external fields, and any other constraints imposed on the system.
If you had a different context in mind when referring to the "boundary value" of a quantum system, please provide more information, and I'll be happy to help clarify further.