It seems there may be a misunderstanding or confusion regarding the nature of quantum mechanics (QM) and its relationship with electrodynamic vector potential. Let's address a few key points:
Compatibility with electrodynamic vector potential: Quantum mechanics is a framework that describes the behavior of particles at the microscopic scale, including electrons and atoms. It is fully compatible with electromagnetism, which includes the concept of the vector potential. In fact, quantum mechanics incorporates electromagnetic interactions through the use of the electromagnetic field and its associated potentials.
Stationary and non-stationary solutions: Quantum mechanics allows for both stationary and non-stationary solutions. Stationary solutions correspond to states with definite energy, where the system remains in a particular energy eigenstate indefinitely. Non-stationary solutions, on the other hand, describe time-dependent behavior and are crucial for understanding dynamic processes.
Completeness of quantum mechanics: Quantum mechanics is considered a complete theory because it provides a comprehensive framework for understanding and predicting the behavior of particles and systems at the quantum level. It successfully describes a wide range of phenomena, from the behavior of atoms and molecules to the properties of elementary particles. Quantum mechanics has been extensively tested and has shown remarkable agreement with experimental observations.
It's worth noting that quantum mechanics does not provide a complete description of all physical phenomena in the universe. For example, it does not currently incorporate gravity, which is described by general relativity. Efforts to reconcile quantum mechanics and general relativity into a more comprehensive theory, such as quantum gravity, are still ongoing.
In summary, quantum mechanics is a well-established and successful theory that is fully compatible with electromagnetism and provides a complete framework for understanding the behavior of particles at the quantum level.