Hamiltonian Help: Learn Physics from Basics

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In summary, the person is asking for book recommendations to learn about Hamiltonians and their eigenvalues. They are specifically interested in a book that covers the basics of these topics, as they have no prior knowledge. The conversation also mentions using Thornton and Marion for classical mechanics, and suggests looking into beginner-level textbooks for quantum mechanics and linear algebra for understanding the diagonalization process.
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bearhug8703
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hey I am i have just finished my final yr from Bangalore.. did phy n maths..interested in pursuing physics in the future.Cld i get some help regarding which books cld b followed if i want to learn Hamiltonian n findin its eigen values. If u cld suggest a book which deals from the basics of the above said ,since i have no knowledge abt the same.
 
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bearhug8703 said:
hey I am i have just finished my final yr from Bangalore.. did phy n maths..interested in pursuing physics in the future.Cld i get some help regarding which books cld b followed if i want to learn Hamiltonian n findin its eigen values. If u cld suggest a book which deals from the basics of the above said ,since i have no knowledge abt the same.

in what context?

if it's hamiltonians classical mechanics, i am unaware of a textbook that discusses eigenvalues of hamiltonians. (i personally used thornton and marion, so the treatment of hamiltonians was basic and minimal.)

if it's quantum mechanics, i am sure that any beginning-level quantum mechanics textbook (griffiths?) discusses this.

as far as the actual process of diagonalization of matrices (ie, finding eigenvalues and eigenvectors), any beginning textbook in linear algebra ought to be sufficient.
 
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Hello! It's great to hear that you are interested in pursuing physics in the future. Learning about Hamiltonian and finding its eigenvalues is an important aspect of physics, and I would be happy to provide some guidance.

First, I would recommend starting with a basic textbook on classical mechanics, as an understanding of this subject is crucial for understanding Hamiltonian. Some good options are "Classical Mechanics" by John R. Taylor or "Introduction to Classical Mechanics" by David Morin.

Next, for a more in-depth understanding of Hamiltonian, I would recommend "Classical Mechanics" by Herbert Goldstein. This book covers the topic extensively and is often used as a textbook in advanced undergraduate and graduate courses.

If you are looking for a more concise and beginner-friendly introduction to Hamiltonian, "Introduction to Hamiltonian Mechanics" by Michael D. Berg is a good option.

Remember to also practice solving problems and doing calculations to solidify your understanding of the concepts. Good luck with your studies!
 

1. What is a Hamiltonian in physics?

A Hamiltonian in physics is a mathematical operator that describes the total energy of a system, including both its potential and kinetic energy. It is commonly used in classical mechanics and quantum mechanics to describe the dynamics of a physical system.

2. What are the basic principles of Hamiltonian mechanics?

The basic principles of Hamiltonian mechanics include the conservation of energy, the principle of least action, and the Hamiltonian equations of motion. It also involves the use of Hamiltonian equations to describe the evolution of a system over time.

3. How is Hamiltonian mechanics different from Lagrangian mechanics?

While both Hamiltonian and Lagrangian mechanics are used to describe the dynamics of physical systems, they differ in the variables they use. Lagrangian mechanics uses generalized coordinates and velocities, while Hamiltonian mechanics uses generalized coordinates and momenta. Additionally, Hamiltonian mechanics includes the concept of energy conservation, which is not explicitly present in Lagrangian mechanics.

4. What are some real-life applications of Hamiltonian mechanics?

Hamiltonian mechanics has a wide range of applications in physics, including classical mechanics, quantum mechanics, and statistical mechanics. It is used to describe the motion of celestial bodies, the behavior of particles in a magnetic field, and the properties of atoms and molecules. It also has applications in fields such as engineering and chemistry.

5. How can I use "Hamiltonian Help: Learn Physics from Basics" to improve my understanding of Hamiltonian mechanics?

"Hamiltonian Help: Learn Physics from Basics" is a comprehensive resource that covers the fundamentals of Hamiltonian mechanics in a clear and concise manner. It includes explanations, examples, and practice problems to help you better understand the concepts. You can use this resource as a supplement to your studies or as a refresher to improve your understanding of Hamiltonian mechanics.

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