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Joker93
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Hello, I really need a good book on ordinary differential equations with applications on Quantum Mechanics, as I will be attending a course on QM but I do not have the proper mathematical background that is needed.
Thank you! Do you know if there is anything else needed for Quantum Mechanics that I should also learn before taking the course?axmls said:Try "Mathematical Methods in the Physical Sciences" by Mary Boas. It's doesn't cover only DEs, but it's got some of everything (at an undergrad level). If you have no exposure to differential equations, you should probably focus on just a differential equations textbook without worrying if it's extremely focused on applications.
I'm of the opinion that you should be comfortable with the math needed in a course before the course starts, because it's a whole lot easier to learn the physics behind something than it is to learn the physics behind something while simultaneously trying to learn the language it's represented in. So I'd say any differential equations textbook would do.
Any differential equations techniques that are needed in quantum mechanics that aren't covered in many DE textbooks will likely be covered in the quantum mechanics textbook anyway.
To be more specific, do you mean having a strong background on eigenvalue problems and matrix operations or do I need more? Also, what about Fourier analysis(and Fourier integrals)?axmls said:If it's a full course on quantum mechanics, it wouldn't hurt to get some background in linear algebra if your linear algebra isn't strong.
The mathematics course that is a prerequisite to the quantum mechanics course does not include partial differential equations, so I expect the professor of the QM course to teach us the basic techniques that will be used in his course.mpresic said:You probably need more partial differential equations rather than differential equations
ODEs are mathematical equations that describe the change of a function over time. They involve the derivative of a function and are commonly used in many areas of science and engineering to model dynamic systems.
ODEs have a wide range of applications, including modeling population growth, predicting weather patterns, analyzing chemical reactions, and understanding the behavior of electric circuits.
Some recommended books on ODEs include "Ordinary Differential Equations" by Morris Tenenbaum and Harry Pollard, "Differential Equations with Applications and Historical Notes" by George F. Simmons, and "Elementary Differential Equations and Boundary Value Problems" by William E. Boyce and Richard C. DiPrima.
To improve your understanding of ODEs, it is important to have a strong foundation in calculus and linear algebra. It can also be helpful to work through practice problems and to seek guidance from a qualified instructor or tutor.
Yes, ODEs are used in many real-world applications. For example, they are used in population ecology to model the growth and decline of animal populations, in economics to study the behavior of stock prices, and in physics to describe the motion of objects under the influence of forces.