Past exam of the chemistry A course of the University of Cambridge / 2024 / Paper 1 / A1 / a / i

Inside the infinite square well, the stationary wavefunctions can be chosen real:They vanish outside the well and at its impenetrable endpoints. A sine meets the left boundary condition; the right one requires $\sin (n\pi )=0$. The putative $n=0$ function is identically zero, so it is not a quantum state. The constants $C_n$ are fixed by wavefunction normalization.