Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the unique mapping relationship between initial and final quantum
  states   In its standard formulation, quantum mechanics presents a very serious
inconvenience: given a quantum system, there is no possibility at all to
unambiguously (causally) connect a particular feature of its final state with
some specific section of its initial state. This constitutes a practical
limitation, for example, in numerical analyses of quantum systems, which often
make necessary the use of some extra assistance from classical methodologies.
Here it is shown how the Bohmian formulation of quantum mechanics removes the
ambiguity of quantum mechanics, providing a consistent and clear answer to such
a question without abandoning the quantum framework. More specifically, this
formulation allows to define probability tubes, along which the enclosed
probability keeps constant in time all the way through as the system evolves in
configuration space. These tubes have the interesting property that once their
boundary is defined at a given time, they are uniquely defined at any time. As
a consequence, it is possible to determine final restricted (or partial)
probabilities directly from localized sets of (Bohmian) initial conditions on
the system initial state. Here, these facts are illustrated by means of two
simple yet physically insightful numerical examples: tunneling transmission and
grating diffraction.

35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex