What are some common perturbation theory problems encountered in quantum mechanics, and what are the solutions to these problems?

Common perturbation theory problems encountered in quantum mechanics include the calculation of energy shifts and wavefunction corrections for a system when a small perturbation is applied. Solutions to these problems involve using perturbation theory formulas to calculate the first-order and higher-order corrections to the energy levels and wavefunctions of the system. These corrections help to account for the effects of the perturbation on the system's behavior and provide a more accurate description of its quantum properties.