Where to learn the matrix formulation of QM

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In summary: Bernard Diu, Frank LaloëIn summary, there are various resources available for learning the matrix way of understanding calculus, including the use of bra-ket notation and lectures from Caltech and the Feynman lectures. The concept of a vector in a given basis and an operator represented as a matrix can also be applied to understanding the Hamiltonian. Additional helpful resources include a tutorial on effective Hamiltonians and the book "Quantum Mechanics" by Claude Cohen-Tannoudji, Bernard Diu, and Frank Laloë.
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Superposed_Cat
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Hi, material on learning the calculus way are plentiful but I can't find anywhere to teach me the matrix way, any links? I can't even find out how to represent the Hamiltonian as a matrix. Thanks in advance
 
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http://www.theory.caltech.edu/people/preskill/ph229/#lecture (Chapter 2)

Take a look also at the third volume of the Feynman lectures.

In a given basis, a vector has a representation as a column vector vi, where i is a discrete index. The number of indices is the dimension of the vector space. You can think of the position space wavefunction ψ(x) similarly as the representation of a vector in the position basis, except that the index x is continuous. Since there are now an infinite number of indices, the dimension of the vector space is infinite. There are differences between finite and infinite dimensional vector spaces, but using the finite dimensional case for intuition is roughly ok. Now sticking to the finite dimensional case, if we think of the state as a column vector in a certain basis, an operator on the state can be represented as a matrix.

For an example of the practical use of the Hamiltonian as a matrix try http://condensedconcepts.blogspot.sg/2013/10/tutorial-on-effective-hamiltonians-for.html
 
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I found most helpful the Quantum Mechanics by Claude Cohen-Tannoudji
 

1. What is the matrix formulation of quantum mechanics?

The matrix formulation of quantum mechanics, also known as the matrix mechanics, is a mathematical formulation of quantum mechanics that uses matrices to represent quantum states and operators. It was developed by Werner Heisenberg and Max Born in the 1920s and was one of the two major formulations of quantum mechanics, along with the wave mechanics.

2. Why is it important to learn the matrix formulation of quantum mechanics?

The matrix formulation of quantum mechanics is important because it provides a mathematical framework for understanding and predicting the behavior of quantum systems. It allows for the calculation of observables, such as energy and position, and provides a way to describe the evolution of quantum states over time.

3. Where can I learn the matrix formulation of quantum mechanics?

The matrix formulation of quantum mechanics is taught in many undergraduate and graduate level physics courses, particularly in courses on quantum mechanics or mathematical methods in physics. It can also be learned through textbooks, online courses, and lectures from experts in the field.

4. Is it necessary to have a strong background in mathematics to learn the matrix formulation of quantum mechanics?

While a strong background in mathematics is helpful, it is not necessary to understand the basics of the matrix formulation of quantum mechanics. Some knowledge of linear algebra and complex numbers is useful, but many resources are available that break down the concepts into more accessible terms for those with less mathematical background.

5. How can I apply the matrix formulation of quantum mechanics in my research or work?

The matrix formulation of quantum mechanics has many practical applications, particularly in fields such as quantum computing, quantum chemistry, and quantum information science. It can also be applied in theoretical research, such as studying the behavior of particles in quantum systems or predicting the outcomes of quantum experiments.

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