Quantum Mechanics: A Mathematical Introduction

This review is written from the perspective of a physical chemist. For someone that needs a "more" mathematically intense (linear algebra based) treatment, but still needs someone to hold there hand while working through some of the unfamiliar math, this is a great book.In the absence of taking a lot of rigorous physics and math courses as a chemist, I needed a bridge from a typical quantum chemistry course to QM at the level of like J.J. Sakurai's "Modern QM" or Cohen-Tannoudji. This book by Dr. Larkoski did exactly that.

This textbook deals with the mathematics used in quantum mechanics. And in doing so it provides an indispensable foundation for understanding quantum mechanics. The book is truly comprehensible. I think it is a wonderful book and definitely worth the money.

I have gone through several QM textbooks in an attempt to learn the subject and found this book annoying at first but eventually came to like it quite a lot. It provides a more mathematical approach to the subject and has some very interesting problems in the homework that it guides the reader through that I have not seen anywhere. As a second text in the subject I like this quite a lot (though I still prefer Zweibach's book as the best comprehensive textbook on the subject) and this could follow after reader Tonwsend perhaps.Quantum mechanics is such a remarkable subject from a physical standpoint but also a mathematical. The math part isn't the hardest and is largely linear algebra and eventually group theory but such a perspective is usually subordinated to the physics on a first attempt to improve intuition building on such an unintuitive subject. This book throws the reader into the math first and subordinates typical solution techniques usually presented like series solutions of the Schrodinger equation to algebraic solutions using Lie theory. The author solves the Hydrogen atom via showing the hidden symmetry from the Runge-Lenz vector and how the solution comes out from being the product of two SU(2) groups. I think if one is presented with this as the solution to the problem at first it would never sink in. Similarly the author introduces some problems that are naturally solved using Baker-Campbell-Haussdorf identities and there is literally no way on a first pass one should be guessing these results to come up with homework solutions. Nonetheless the material, if one is familiar is quite cool, for example there is a problem on the fractal dimension of a quantum particle that follows from the uncertainty principle one has to walk through. These are the sorts of problems I assume the author liked to introduce to display the more mathematical side of the subject.The topics on approximation techniques is ok, Zweibach is much better on perturbation theory. The author introduces some matrix power techniques I have not seen before but they seem pretty useless in practice and most of the coverage is too brief including the WKB approximation. I think the author should have covered more complex analysis more thoroughly to introduce some of the ideas on poles in a more complete fashion. There are some incorrect statements in the book like two groups with the same lie algebra are isomorphic which is false given SO(3) and SU(2) share the same lie algebra. There are a few other mis-statements interspersed on some algebra topics but nothing that damages the core text.Overall strong book that is quite unique in its approach. Its uniqueness makes it unclear who the audience should be. As mentioned I prefer Zweibach which i think is both mathematical and far more complete with both the typical solutions to the hydrogen atom and harmonic oscillator through series solutions but also the algebraic solutions as well as superpotentials. That book is just much longer though. Nonetheless I think as a second book on quantum mechanics this book might be of use or probably most likely as a supplemental text for people with standard textbooks which are missing some mathematical details that this provides without getting into the likes of physics books for mathematicians which are too dry.

There are many ways to introduce quantum mechanics, but I've never seen it done quite like this. Larkoski starts with the simplest statement of QM's axioms (roughly, that observables are eigenvalues of Hermitian operators acting in Hilbert space), and works backward to develop the mathematical basis and physical motivation for these axioms. Schrödinger's Equation is then finally reached Chapter 4. I find the approach most reminiscent of Landau and Lifshitz's classic texts, and while this is a clearer and more modern presentation, I suspect it will have many of the same fans and detractors. This would be a great intro book for advanced and mathematically-minded undergraduates, as well as a solid supplement for graduate students looking to deepen their understanding. A contemporary presentation of quantum mechanics, stripped to the beauty of its mathematical essence.

The media could not be loaded. Recebi agora mesmo. Livro de capa dura, impressão de excelente qualidade.

“One approach to quantum mechanics is just to identify the Schrodinger equation as a second-order linear differential equation for the wave function, and then go to town finding its closed-form solutions, by hook or by crook. However, there is no physics in doing this and quantum mechanics is fundamentally not a theory of differential equations. It is a theory in which linear operators and vector spaces and eigenvalues are central. So, while solving differential equations is very concrete and teaches students useful mathematical tools and tricks, it is not quantum mechanics.”Andrew J. Larkoski