%0 Journal Article
%T Explanation of Relation between Wave Function and Probability Density Based on Quantum Mechanics in Phase Space
%A Chol Jong
%A Jin-Sim Kim
%A Shin-Hyok Jon
%A Son-Il Jo
%J World Journal of Mechanics
%P 20-72
%@ 2160-0503
%D 2023
%I Scientific Research Publishing
%R 10.4236/wjm.2023.131002
%X The main problem of quantum mechanics is to
elucidate why the probability density is the modulus square of wave function.
For the purpose of solving this problem, we explored the possibility of
deducing the fundamental equation of quantum mechanics by starting with the
probability density. To do so, it is necessary to formulate a new theory of
quantum mechanics distinguished from the previous ones. Our investigation shows
that it is possible to construct quantum mechanics in phase space as an
alternative autonomous formulation and such a possibility enables us to study
quantum mechanics by starting with the probability density rather than the wave
function. This direction of research is contrary to configuration-space formulation
of quantum mechanics starting with the wave function. Our work leads to a full
understanding of the wave function as the both mathematically and physically
sufficient representation of quantum-mechanical state which supplements
information on quantum state given solely by the probability density with phase
information on quantum state. The final result of our work is that quantum
mechanics in phase space satisfactorily elucidates the relation between the
wave function and the probability density by using the consistent procedure
starting with the probability density, thus corroborating the ontological
interpretation of the wave function and withdrawing a main assumption of
quantum mechanics.
%K Quantum Ensemble Theory
%K Quantum Mechanics In Phase Space
%K Wave Function
%K Probability Density
%K Schrö
%K dinger Equation
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=122548