Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Mechanics   I consider in this book a formulation of Quantum Mechanics. Usually QM is
formulated based on the notion of time and space, both of which are thought a
priori given quantities or notions. However, when we try to define the notion
of velocity or momentum, we encounter a difficulty as we will see in chapter 1.
The problem is that if the notion of time is given a priori, the velocity is
definitely determined when given a position, which contradicts the uncertainty
principle of Heisenberg. We then set the basis of QM on the notion of position
and momentum operators as in chapter 2. Time of a local system then is defined
approximately as a ratio $|x|/|v|$ between the space coordinate $x$ and the
velocity $v$. In this formulation of QM, we can keep the uncertainty principle,
and time is a quantity that does not have precise values unlike the usually
supposed notion of time has. The feature of local time is that it is a time
proper to each local system, which is defined as a finite set of quantum
mechanical particles. We now have an infinite number of local times that are
unique and proper to each local system. Based on the notion of local time, the
motion inside a local system is described by the usual Schr\"odinger equation.
We investigate such motion in a given local system in part II. This is a usual
quantum mechanics. After some excursion of the investigation of local motion,
we consider in part III the relative relation or motion between plural local
systems. In the final part IV, we will prove that there is at least one
Universe wave function $\phi$ in which all local systems have local motions and
thus local times. This concludes our formulation of Quantum Mechanics.

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The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
3
The categories of this paper are: physics