Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solving the time-dependent Schr\"odinger equation via Laplace transform   We show how the Laplace transform can be used to give a solution of the
time-dependent Schr\"odinger equation for an arbitrary initial wave packet if
the solution of the stationary equation is known. The solution is obtained
without summing up eigenstates nor do we need the path integral. We solve the
initial value problem for three characteristic piecewise constant potentials.
The results give an intuitive picture of the wave packet dynamics, reproducing
explicitly all possible reflection and transmission processes. We investigate
classical and quantum properties of the evolution and determine the reflection
and transmission probabilities.

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The categories of this paper are: cond-mat
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The categories of this paper are: eess
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph