Abstract
The time-independent Schrödinger equation is the one place where stationary states can be produced as solutions of the equation. The time-dependent Schrödinger equation plays the role of the “equation of motion,” describing the evolution of a given wave function as time passes. As always for an equation of motion, one has to provide an initial state (starting point), i.e., the wave function for t=0. Both the stationary states and the evolution of the nonstationary states depend on the energy operator (Hamiltonian). If one finds some symmetry of the Hamiltonian, this will influence the symmetry of the wave functions. At the end of this chapter we will be interested in the evolution of a wave function after applying a perturbation.
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