The most important open problem of the studies of quantum mechanics is to elucidate why probability density is the modulus square of a wave function.
This problem has been a fundamental subject of a long-standing debate that began soon after quantum theory was basically formulated in 1920s.
Within the framework of the standard theory of quantum mechanics, the relation between wave function and probability density is assumed rather than derived.
Successful works which aim to elucidate this assumption theoretically are not yet known.
This problem is related to in what space quantum mechanics should be constructed.
For the purpose of solving this problem, Jong Chol, a researcher at the Faculty of Materials Science and Technology, has deduced a fundamental equation of quantum mechanics by starting with probability density.
To do so, it was necessary for him to formulate a new theory of quantum mechanics distinguished from the previous ones. His investigation shows that it is possible to construct quantum mechanics in phase space as an alternative autonomous formulation and such possibility enables us to study quantum mechanics by starting with probability density rather than wave function.
This direction of research is contrary to configuration-space formulation of quantum mechanics starting with wave function.
The work leads to a full understanding of the wave function as mathematically and physically sufficient representation of quantum-mechanical state which supplements information on quantum state given solely by probability density with phase information on quantum state.
The final result of the work is that quantum mechanics in phase space satisfactorily elucidates the relation between wave function and probability density by using the consistent procedure starting with probability density, thus withdrawing a main assumption of quantum mechanics.
You can find more information about this in his paper “Explanation of Relation between Wave Function and Probability Density Based on Quantum Mechanics in Phase Space” in “World Journal of Mechanics”.
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