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1

Selvadurai, A. P. S. Partial Differential Equations in Mechanics 1: Fundamentals, Laplace's Equation, Diffusion Equation, Wave Equation. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000.

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2

Berezin, F. A. The Schrödinger equation. Dordrecht: Kluwer Academic Publishers, 1991.

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3

Bittanti, Sergio. The Riccati Equation. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991.

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4

Anikonov, D. S. Transport equation and tomography. Utrecht: VSP, 2002.

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5

The porous medium equation: Mathematical theory. Oxford: Clarendon, 2007.

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6

A, Bollen Kenneth, and Long J. Scott, eds. Testing structural equation models. Newbury Park: Sage Publications, 1993.

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7

Lettau, Martin. Euler equation errors. Cambridge, MA: National Bureau of Economic Research, 2005.

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8

M, Jimbo, ed. Yang-Baxter equation in integrablesystems. Singapore: World Scientific, 1990.

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9

Hong, Sung-Min. Deterministic solvers for the Boltzmann transport equation. Wein: Springer, 2011.

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10

M, Jimbo, ed. Yang-Baxter equation in integrable systems. Singapore: World Scientific, 1990.

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11

Wolfgang, Stiller. Arrhenius equation and non-equilibrium kinetics: 100 years Arrhenius equation. Leipzig: BSB B.G. Teubner, 1989.

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12

Structural equation modeling: Foundations and extensions. 2nd ed. Thousand Oaks: Sage Publications, 2009.

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13

Popivanov, Peter R. Nonlinear waves: An introduction. Singapore: World Scientific, 2011.

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14

J, Shih T., and United States. National Aeronautics and Space Administration., eds. A critical comparison of two-equation turbulence models. [Washington, DC]: National Aeronautics and Space Administration, 1991.

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15

Devaney, Anthony J. Mathematical foundations of imaging, tomography and wavefield inversion. Cambridge: Cambridge University Press, 2012.

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16

Structural equation modeling for social and personality psychology. London: SAGE, 2011.

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17

Glenn, Fulford, ed. Mathematical modelling with case studies: A differential equation approach using Maple. London: Taylor & Francis, 2002.

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18

1951-, Pugesek Bruce H., Tomer Adrian, and Eye Alexander von, eds. Structural equation modeling: Applications in ecological and evolutionary biology. Cambridge, UK: Cambridge University Press, 2003.

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19

The Duffing equation: Nonlinear oscillators and their phenomena. Chichester, West Sussex, U.K: Wiley, 2011.

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20

Tsutomu, Kitoh, ed. Introduction to optical waveguide analysis: Solving Maxwell's equations and the Schrödinger equation. New York: J. Wiley, 2001.

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21

The Fokker-Planck equation: Methods of solution and applications. 2nd ed. New York: Springer-Verlag, 1996.

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22

Risken, H. The Fokker-Planck equation: Methods of solution and applications. 2nd ed. Berlin: Springer-Verlag, 1989.

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23

Stephen, Wiggins, ed. Invariant manifolds and fibrations for perturbed nonlinear Schrödinger equations. New York: Springer, 1997.

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24

Balance equation approach to electron transport In semiconductors. Hackensack, NJ: World Scientific, 2008.

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25

N, Bellomo, and Arlotti L, eds. Lecture notes on the mathematical theory of the Boltzmann equation. Singapore: World Scientific, 1995.

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26

N, Bellomo, ed. Mathematical topics in nonlinear kinetic theory II: The Enskog equation. Singapore: World Scientific, 1991.

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27

H, Hoyle Rick, ed. Structural equation modeling: Concepts, issues, and applications. Thousand Oaks: Sage Publications, 1995.

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28

Vazquez, Juan Luis. Porous Medium Equation: Mathematical Theory. Oxford University Press, 2006.

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29

Inc, Design Science. Mathtype: The Mathematical Equation Editor. Springer-Verlag, 2004.

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30

Vazquez, Juan Luis. Porous Medium Equation: Mathematical Theory. Ebsco Publishing, 2006.

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31

Kim, Doyun. Mathematical Structures and Equation Poetry. Independently Published, 2017.

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32

Mann, Peter. Wave Mechanics & Elements of Mathematical Physics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0005.

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Abstract:
This chapter presents an in-depth look at classical wave mechanics and mathematical physics, containing key examples directly relevant to molecular physics. The separation of variables is used to construct the Helmholtz equation from the one-dimensional wave equation before considering the three-dimensional wave equation. From this, equations for the temporal, radial, azimuth and angular components are developed and solutions using the Bessel equations and Legendre polynomials are found. Boundary conditions are explained and the Rayleigh plane wave expansion as the general solution to the Helmholtz equation is reconstructed. Both the Hermite equation and the Legendre equation are derived using the series solution method, and the Laplace equation is discussed.
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33

Vazquez, Juan Luis. The Porous Medium Equation: Mathematical Theory (Oxford Mathematical Monographs). Oxford University Press, USA, 2006.

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34

Guo, Boling, Xiaoyu Xi, Bingqiang Xie, Guangwu Wang, and Dongfen Bian. Quantum Hydrodynamics Equation. de Gruyter GmbH, Walter, 2021.

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35

Guo, Boling, Xiaoyu Xi, Bingqiang Xie, Guangwu Wang, and Dongfen Bian. Quantum Hydrodynamics Equation. de Gruyter GmbH, Walter, 2021.

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36

Shubin, M. A., and F. A. Berezin. The Schrödinger Equation (Mathematics and its Applications). Springer, 1991.

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37

Price, Lionel S. Wave Equation: An Overview. Nova Science Publishers, Incorporated, 2020.

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38

Price, Lionel S. Wave Equation: An Overview. Nova Science Publishers, Incorporated, 2020.

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39

Long, J. Scott, and Kenneth A. Bollen. Testing Structural Equation Models. SAGE Publications, Incorporated, 2012.

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40

Differential Equation Models in Epidemiology. Brazil: Editora do IMPA, 2021.

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41

Guo, Boling. Quantum Hydrodynamic Equation and Its Mathematical Theory. World Scientific Pub Co Inc, 2022.

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42

Duncan, Otis Dudley. Introduction to Structural Equation Models. Elsevier Science & Technology Books, 2014.

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43

Shimizu, Shohei. Semiparametric Structural Equation Models for Causal Discovery. Springer London, Limited, 2017.

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44

Shimizu, Shohei. Semiparametric Structural Equation Models for Causal Discovery. Springer, 2021.

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45

Pankov, Alexander. Lecture Notes on Schrodinger Equations (Contemporary Mathematical Studies). Nova Science Pub Inc, 2008.

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46

1947-, Galdi Giovanni P., ed. Mathematical problems relating to the Navier-Stokes equation. Singapore: World Scientific, 1992.

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47

Kawano, Kenji, and Tsutomu Kitoh. Introduction to Optical Waveguide Analysis: Solving Maxwell's Equation and the Schrdinger Equation. Wiley-Interscience, 2001.

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48

America, Mathematical Association of. American Mathematical Monthly: The Official Journal of the Mathematical Association of America; Volume 8. Creative Media Partners, LLC, 2018.

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49

America, Mathematical Association of. American Mathematical Monthly: The Official Journal of the Mathematical Association of America; Volume 8. Creative Media Partners, LLC, 2018.

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50

America, Mathematical Association of. American Mathematical Monthly: The Official Journal of the Mathematical Association of America; Volume 29. Creative Media Partners, LLC, 2018.

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