If we try to describe an electron in an atom using only one wavefunction, we would not be able to fully capture the behavior of the electron. The wavefunction of an electron in an atom is described by the Schrödinger's equation, which is a partial differential equation that accounts for the wave-like nature of particles.
In the context of an atom, the electron's behavior is determined by its energy level, angular momentum, and other quantum mechanical properties. These properties are quantized, meaning they can only take on specific discrete values. The wavefunction of an electron in an atom is actually a combination of multiple wavefunctions, each corresponding to a specific energy level and angular momentum state.
This combination of wavefunctions is known as an atomic orbital. Each atomic orbital corresponds to a specific electron energy level and shape, such as s, p, d, or f orbitals. The atomic orbitals provide information about the probability distribution of finding an electron at a particular location around the nucleus.
Using only one wavefunction would fail to capture the full range of possible energy levels and angular momentum states that an electron can occupy. It would not accurately describe the electron's behavior, energy levels, and probability distribution within the atom.
To properly describe an electron in an atom, we need to consider the complete set of wavefunctions or atomic orbitals associated with the different energy levels and angular momentum states. This allows us to obtain a more comprehensive understanding of the electron's behavior and its interactions with the nucleus and other electrons in the atom.