python - Python如何读取带有方程式的乳胶生成的pdf

Question

考虑以下文章

https://arxiv.org/pdf/2101.05907.pdf

这是一篇典型格式的学术论文，pdf 文件中只有两张图片。

以下代码用于从论文中提取文本和方程式

#Related code explanation: https://stackoverflow.com/questions/45470964/python-extracting-text-from-webpage-pdf
import io
import requests
r = requests.get(url)
f = io.BytesIO(r.content)

#Related code explanation: https://stackoverflow.com/questions/45795089/how-can-i-read-pdf-in-python
import PyPDF2
fileReader = PyPDF2.PdfFileReader(f)

#Related code explanation: https://automatetheboringstuff.com/chapter13/
print(fileReader.getPage(0).extractText())

然而，结果并不完全正确

Bohmpotentialforthetimedependentharmonicoscillator
FranciscoSoto-Eguibar
1
,FelipeA.Asenjo
2
,SergioA.Hojman
3
andH
´
ectorM.
Moya-Cessa
1
1
InstitutoNacionaldeAstrof´
´
OpticayElectr´onica,CalleLuisEnriqueErroNo.1,SantaMar´Tonanzintla,
Puebla,72840,Mexico.
2
FacultaddeIngenier´yCiencias,UniversidadAdolfoIb´aŸnez,Santiago7491169,Chile.
3
DepartamentodeCiencias,FacultaddeArtesLiberales,UniversidadAdolfoIb´aŸnez,Santiago7491169,Chile.
DepartamentodeF´FacultaddeCiencias,UniversidaddeChile,Santiago7800003,Chile.
CentrodeRecursosEducativosAvanzados,CREA,Santiago7500018,Chile.
Abstract.
IntheMadelung-Bohmapproachtoquantummechanics,weconsidera(timedependent)phasethatdependsquadrati-
callyonpositionandshowthatitleadstoaBohmpotentialthatcorrespondstoatimedependentharmonicoscillator,providedthe
timedependentterminthephaseobeysanErmakovequation.
Introduction
Harmonicoscillatorsarethebuildingblocksinseveralbranchesofphysics,fromclassicalmechanicstoquantum
mechanicalsystems.Inparticular,forquantummechanicalsystems,wavefunctionshavebeenreconstructedasisthe
caseforquantizedincavities[1]andforion-laserinteractions[2].Extensionsfromsingleharmonicoscillators
totimedependentharmonicoscillatorsmaybefoundinshortcutstoadiabaticity[3],quantizedpropagatingin
dielectricmedia[4],Casimire

ect[5]andion-laserinteractions[6],wherethetimedependenceisnecessaryinorder
totraptheion.
Timedependentharmonicoscillatorshavebeenextensivelystudiedandseveralinvariantshavebeenobtained[7,8,9,
10,11].Alsoalgebraicmethodstoobtaintheevolutionoperatorhavebeenshown[12].Theyhavebeensolvedunder
variousscenariossuchastimedependentmass[12,13,14],timedependentfrequency[15,11]andapplicationsof
invariantmethodshavebeenstudiedindi

erentregimes[16].Suchinvariantsmaybeusedtocontrolquantumnoise
[17]andtostudythepropagationoflightinwaveguidearrays[18,19].Harmonicoscillatorsmaybeusedinmore
generalsystemssuchaswaveguidearrays[20,21,22].
Inthiscontribution,weuseanoperatorapproachtosolvetheone-dimensionalSchr
¨
odingerequationintheBohm-
Madelungformalismofquantummechanics.ThisformalismhasbeenusedtosolvetheSchr
¨
odingerequationfor
di

erentsystemsbytakingtheadvantageoftheirnon-vanishingBohmpotentials[23,24,25,26].Alongthiswork,
weshowthatatimedependentharmonicoscillatormaybeobtainedbychoosingapositiondependentquadratictime
dependentphaseandaGaussianamplitudeforthewavefunction.Wesolvetheprobabilityequationbyusingoperator
techniques.Asanexamplewegivearationalfunctionoftimeforthetimedependentfrequencyandshowthatthe
Bohmpotentialhasdi

erentbehaviorforthatfunctionalitybecauseanauxiliaryfunctionneededinthescheme,
namelythefunctionsthatsolvestheErmakovequation,presentstwodi

erentsolutions.
One-dimensionalMadelung-Bohmapproach
ThemainequationinquantummechanicsistheSchrodingerequation,thatinonedimensionandforapotential
V
(
x
;
t
)
iswrittenas(forsimplicity,weset
}
=
1)
i
@ 
(
x
;
t
)
@
t
=

1
2
m
@
2
 
(
x
;
t
)
@
x
2
+
V
(
x
;
t
)
 
(
x
;
t
)
(1)
arXiv:2101.05907v1  [quant-ph]  14 Jan 2021

如图所示：

1. 诸如标题之类的间距消失了，导致字符串的含义减少。
2. 乳胶方程式是错误的，并且在第二页上变得更糟。

如何解决此问题并从乳胶生成的 pdf 文件中正确提取文本和方程式？

标签： pythonpdftextlatexpypdf2