Hi all, I have a question about Slater Determinant for excited states. Let's say we want to construct approximate (2 level) wavefunction of He in some certain state. Since we have two electrons in two level system with spin in consideration, we can construct total of 4 different wavefunctions corresponding to each of the states. So by constructing Slater Determinant, we should be able to achieve wavefunctions for each of these 4 different states with anti-symmetry in consideration. However, in order to achieve the "correct" wavefunction of a state (for example, excited singlet state), we sometimes need linear combination of the Slater Determinant. However, in cases like ground state, only single Slater Determinant is required. QUESTION: How do we know whether a wavefunction constructed simply from Slater Determinant is "correct" or "not correct"? In another words, how do we know if we need linear combination of Slater Determinant or not?