When we use the term wave function we normally mean the function that is a solution to the Schrodinger equation, and particle creation and annihilation does not exist in the Schrodinger approach. So by definition the Schrodinger wave function cannot describe any process in which articles are created or destroyed.
To understand creation and annihilation we need to use quantum field theory. The difference in this approach is that particles are no longer fundamental objects. Instead they are excitations of a quantum field and they can be created by adding energy to the field and destroyed by removing energy from the field.
The idea of a wave function does not really exist in quantum field theory. The individual particles can be approximately described by a one particle wave function as long as the particles do not interact with any other particles. In this case the particles are described by functions called Fock states. However this is only an approximation since all real particles interact with each other and the interaction mixes up their states.