Home > Conscious > Chapter 9 > 9.2. Eigenstates (Eigenfunctions) 

Twostate SystemA quantum system may have two or more eigenstates (or eigenfunctions), each is a solution of the Schrödinger Equation  a fundamental equation in quantum mechanics. An eigenstate is the state that can actually be observed. Since all eigenstates are the solutions of the Schrödinger Equation, their superposition Ψ (called wavefunction) is also a solution. For a system with two eigenstates, Φ_{1} and Φ_{2}, Ψ may be written as Ψ = a_{1} Φ_{1} + a_{2} Φ_{2} where a_{1} and a_{2} are the probability amplitudes. That means, the probability for the system to be in Φ_{1} or Φ_{2} is a_{1}^{2} or a_{2}^{2}, respectively. Atomic OrbitalsThe system consisting of an electron surrounding an atomic nucleus has numerous eigenstates. Each eigenstate is characterized by three quantum numbers: n, ℓ, and m. These eigenstates are also called orbitals. The s orbital, p orbital and d orbital refer to the eigenstates with ℓ = 0, 1 and 2 respectively (Figure 91). Mathematically, the eigenfunctions can be represented by spherical harmonics Y_{ℓm}(θ, φ), which have aso been used to describe the scalp electric potentials measured by EEG (Section 9.3). Figure 91. Atomic orbitals.
