(Solved): particle on a ring The general form of the wavefunction of a particle on a ring is: \( \psi(\phi)=N ...

The general form of the wavefunction of a particle on a ring is: \( \psi(\phi)=N e^{\pm i \alpha \phi} \) The boundary condition is: \( \psi(\phi)=\psi(\phi+2 n \pi) \) \( \& \) applying the boundary condition and focusing on the imaginary part of the wavefunction gives \( N \cos (\alpha \phi)=N \cos (\alpha(\phi+2 n \pi)) \) Starting from this equation, show that the wavefunction can be written as: \( \psi=N e^{i m_{l} \phi} \), where \( m_{l} \) is an integer.