Hydrogen in a cavity

The system of a proton and an electron in an inert and impenetrable spherical cavity is studied by solving Schr"{o}dinger equation with the correct boundary conditions. The differential equation of a hydrogen atom in a cavity is derived. The numerical results are obtained with the help a power and efficient few-body method, Gaussian Expansion Method. The results show that the correct implantation of the boundary condition is crucial for the energy spectrum of hydrogen in a small cavity.