ralqs said:I just finished a course on linear algebra. The class was quite slow, and not much material was covered (essentially going as far as diagonalization w/ some applications). Seeing as I will be taking a QM course next semester, I thought that it might be a good idea to advance myself on the math behind QM over the summer. Could someone recommend a suitable advanced linear algebra text that would be appropriate for QM?
I skimmed through it, and although it seems good, I'm always a little suspect of physics texts that try to teach math. My experience is that they are generally rushed, and important ideas and concepts are missed in the process. Would you happen to know a book exclusively dedicated to the same topics, but more thorough?totentanz said:Try the first chapter of "Principles of Quantum Mechanics - R. Shankar" called Mathematical introduction,and you will know exactly what you are going to learn
That stuff I know already. My linear prof had promised, in the beginning of the course, to discuss infinite-dimensional vector spaces, as well as certain types of matrices and their properties (ie hermitean, adjoint, etc.)Fredrik said:I think Axler is excellent for QM. You should stay away from books that delay the introduction of linear transformations/operators instead of introducing them early. For example, Anton defines them around page 300, which is just ridiculous. Make sure you understand the relationship between linear operators and matrices (i.e. this) perfectly.
ralqs said:I skimmed through it, and although it seems good, I'm always a little suspect of physics texts that try to teach math. My experience is that they are generally rushed, and important ideas and concepts are missed in the process. Would you happen to know a book exclusively dedicated to the same topics, but more thorough?
ralqs said:I skimmed through it, and although it seems good, I'm always a little suspect of physics texts that try to teach math. My experience is that they are generally rushed, and important ideas and concepts are missed in the process. Would you happen to know a book exclusively dedicated to the same topics, but more thorough?
That stuff I know already. My linear prof had promised, in the beginning of the course, to discuss infinite-dimensional vector spaces, as well as certain types of matrices and their properties (ie hermitean, adjoint, etc.)
ralqs said:I skimmed through it, and although it seems good, I'm always a little suspect of physics texts that try to teach math. My experience is that they are generally rushed, and important ideas and concepts are missed in the process. Would you happen to know a book exclusively dedicated to the same topics, but more thorough?
Linear algebra is the mathematical language used to describe the behavior of quantum systems. It is a fundamental tool in understanding the principles and calculations involved in quantum mechanics.
The key concepts include vector spaces, matrices, eigenvalues and eigenvectors, unitary transformations, and inner product spaces. These concepts are used to represent and manipulate quantum states and operators.
Quantum superposition is the principle that a quantum system can exist in multiple states at the same time. This can be represented using linear algebra by combining two or more quantum states through the use of vector addition and scalar multiplication.
Yes, linear algebra is a powerful tool for solving problems in quantum mechanics. It allows for the manipulation and transformation of quantum states and operators, making it possible to calculate probabilities and predict the behavior of quantum systems.
There are many textbooks, online courses, and video lectures available for learning linear algebra for quantum mechanics. Some recommended resources include "Quantum Computation and Quantum Information" by Nielsen and Chuang and "Quantum Mechanics for Scientists and Engineers" by David Miller.