Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical approach to quantum mechanics I: General nonrelativistic
  theory   In this initial paper in a series, we first discuss why classical motions of
small particles should be treated statistically. Then we show that any
attempted statistical description of any nonrelativistic classical system
inevitably yields the multi-coordinate Schr\"odinger equation, with its usual
boundary conditions, as an essential statistical equation for the system. We
derive the general "canonical quantization" rule, that the Hamiltonian operator
must be the classical Hamiltonian in the $N$-dimensional metric configuration
space defined by the classical kinetic energy of the system, with the classical
conjugate momentum $N$-vector replaced by $-i\hbar$ times the vector gradient
operator in that space. We obtain these results by using conservation of
probability, general tensor calculus, the Madelung transform, the Ehrenfest
theorem and/or the Hamilton-Jacobi equation, and comparison with results for
the charged harmonic oscillator in stochastic electrodynamics. We also provide
two illustrative examples and a discussion of how coordinate trajectories could
be compatible with wave properties such as interference, diffraction, and
tunneling.

30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th