Abstract
The definition of momentum operator in quantum mechanics has some foundational problems and needs to be improved. For example, the results are different in general by using momentum operator and kinetic operator to calculate microparticle’s kinetic energy. In the curved coordinate systems, momentum operators can not be defined properly. When momentum operator is acted on non-eigen wave functions in coordinate space, the resulting non-eigen values are complex numbers in general. In this case, momentum operator is not the Hermitian operator again. The average values of momentum operator are complex numbers unless they are zero. The same problems exist for angle momentum operator. Universal momentum operator is proposed in this paper. Based on it, all problems above can be solved well. The logical foundation of quantum mechanics becomes more complete and the EPY momentum paradox can be eliminated thoroughly. By considering the fact that there exist a difference between the theoretical value and the real value of momentum, the concepts of auxiliary momentum and auxiliary angle momentum are introduced. The relation between auxiliary angle momentum and spin is deduced and the essence of micro-particle’s spin is revealed. In this way, the fact that spin gyro-magnetic ratio is two times of orbit gyro-magnetic ratio, as well as why the electrons of ground state without obit angle momentum do not fall into atomic nuclear can be explained well. The real reason that the Bell inequality is not supported by experiments is revealed, which has nothing to do with whether or not hidden variables exist, as well as whether or not locality is violated in microcosmic processes.
Highlights
Since quantum mechanics was established, its correctness has been well verified
Due to the incompleteness of angle momentum operator in quantum mechanics, we introduce the concept of spin
According to current quantum mechanics, when the operator is acted on non-eigen function, non-eiegn values and average values of momentum operator are complex numbers in general
Summary
Since quantum mechanics was established, its correctness has been well verified. But there exists serious controversy on its physical significance. With operators of quantum mechanics acting on the eigen functions, we obtain real eigen values. If operators act on the non-eigen functions, the results are complex numbers in general. We have to consider a non-free particle, for example an electron in the ground state of hydrogen, as the sum of infinite numbers of free electrons with different momentums. This result is difficult in constructing a physical image, thought it is legal in mathematics. Some operators of quantum mechanics have no proper eigen functions, for example, angle momentum operator Lx , Ly and Lz in rectangular coordinate system. When universal momentum operator is acted on arbitrary non-eigen wave functions, the non-eigen values are real numbers. Because kinetic operator is aright, we have to improve momentum operator to make it consistent with kinetic operator
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
