Resources for variational principle to solve coulomb problem in D dimension

In summary, the conversation was about the struggle to find good resources on variational principle, with the person having an instructor who does not teach and only tells them to search the internet on their own. The person has found various readings but is in need of resources specifically on physical applications of variational principle, such as solving the Coulomb problem in D dimension and Gram-schmidt integration process. Some potential resources were suggested, including lecture notes, books, and textbooks, all available on different platforms such as ArXiv, Amazon, and Google Books.
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Hi, i have been struggling to find some good resources on variational principle , I have got an instructor in advanced quantum course who just have one rule for teaching students- "dig the Internet and I don't teach you anything".. So I digged a lot and came up with a lot reading but I need particular resources that deals with physical application like solving Coulomb problem in D dimension, Gram-schimdt integration process etc.
 
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Any help will be appreciated.Here are some resources that may help you with variational principle and its physical applications:1. Lecture Notes on Variational Principles in Physics by J. Mathews (available on ArXiv): https://arxiv.org/abs/physics/01100932. Variational Principles in Quantum Mechanics by J. L. Safko (available on Amazon): https://www.amazon.com/dp/0849392871/?tag=pfamazon01-20. Introduction to the Variational Method in Quantum Mechanics by J. D. Anderson (available on Google Books): https://books.google.com/books?id=5...iational principle quantum mechanics&f=false4. Variational Principles of Mechanics by V. I. Arnold (available on Amazon): https://www.amazon.com/dp/0486412279/?tag=pfamazon01-20. Variational Principles and Methods in Theoretical Physics by M. Gell-Mann and J. B. Hartle (available on Amazon): https://www.amazon.com/dp/0521393960/?tag=pfamazon01-20. A First Course in Variational Principles and Optimal Control Theory by J. H. van Schagen (available on Amazon): https://www.amazon.com/dp/3527631445/?tag=pfamazon01-20
 

FAQ: Resources for variational principle to solve coulomb problem in D dimension

1. What is the variational principle?

The variational principle is a fundamental concept in physics and mathematics that states that the true solution to a problem is the one that minimizes a certain functional (a function of functions). In other words, it is a way to find the most optimal solution to a problem.

2. How does the variational principle help solve the Coulomb problem?

The Coulomb problem involves finding the motion of a charged particle in an electrostatic field. By applying the variational principle, we can find the most optimal path for the particle to take in order to minimize its potential energy and solve the problem.

3. What is the significance of the D dimension in the Coulomb problem?

The Coulomb problem can be solved in any number of dimensions, denoted by D. The D dimension is important because it determines the number of variables needed to fully describe the problem. For example, in 3 dimensions (D=3), we need the x, y, and z coordinates to describe the particle's position, while in 2 dimensions (D=2), only the x and y coordinates are needed.

4. What are some common resources for learning about the variational principle and solving the Coulomb problem?

There are many resources available for learning about the variational principle and solving the Coulomb problem, including textbooks, online tutorials, and academic papers. Some recommended resources include "Introduction to Classical Mechanics" by David Morin and "Variational Principles of Mechanics" by Cornelius Lanczos.

5. Are there any practical applications of the variational principle and solving the Coulomb problem?

Yes, the variational principle and solving the Coulomb problem have several practical applications in physics and engineering. For example, it can be used to study the behavior of charged particles in electric fields, to model the motion of celestial bodies in gravitational fields, and to optimize the design of electronic circuits.

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