The wave-particle duality in quantum mechanics is a fundamental aspect of the theory that has been extensively studied and explored since its inception. However, it is important to note that the wave-particle duality is not considered a problem in the sense of a contradiction or inconsistency in the theory. Instead, it is a fundamental feature of quantum mechanics that has been experimentally verified and is supported by a wealth of evidence.
Quantum mechanics provides a mathematical framework that successfully describes the behavior of particles at the microscopic level. It allows us to make highly accurate predictions and has been confirmed by numerous experiments. The wave-particle duality, as described by the mathematical formalism of quantum mechanics, provides a comprehensive understanding of the behavior of particles in various experimental setups.
That said, there have been ongoing philosophical debates and discussions regarding the interpretation of wave-particle duality and the nature of particles at the quantum level. Different interpretations, such as the Copenhagen interpretation, the pilot-wave theory (also known as the de Broglie-Bohm interpretation), or the many-worlds interpretation, offer different perspectives on how to understand and interpret the underlying reality described by quantum mechanics.
However, it's important to note that these interpretations go beyond the mathematical framework of quantum mechanics itself and involve philosophical considerations. Currently, there is no universally accepted interpretation that fully resolves all the questions and debates surrounding the wave-particle duality. The interpretation of quantum mechanics remains an active area of research and a subject of ongoing discussion and exploration among physicists and philosophers.