By Barry G. Adams
This e-book presents an advent to using algebraic equipment and sym bolic computation for easy quantum structures with functions to massive order perturbation idea. it's the first ebook to combine Lie algebras, algebraic perturbation concept and symbolic computation in a kind appropriate for college students and researchers in theoretical and computational chemistry and is with ease divided into elements. the 1st half, Chapters 1 to six, presents a pedagogical creation to the real Lie algebras so(3), so(2,1), so(4) and so(4,2) wanted for the learn of straightforward quantum platforms akin to the D-dimensional hydrogen atom and harmonic oscillator. This fabric is acceptable for complicated undergraduate and starting graduate scholars. Of specific value is using so(2,1) in bankruptcy four as a spectrum producing algebra for a number of very important platforms corresponding to the non-relativistic hydrogen atom and the relativistic Klein-Gordon and Dirac equations. This method offers an attractive and significant substitute to the standard textbook strategy utilizing sequence recommendations of differential equations.
Read Online or Download Algebraic Approach to Simple Quantum Systems: With Applications to Perturbation Theory PDF
Similar quantum theory books
During this variation now we have rewritten the chapters that debate the equipment of continuing integration and the renormalization staff, that are subject matters in conception that experience develop into vitally important lately. we have now additionally remodeled and supplemented the sections at the entire eco-friendly capabilities.
The quantum inverse scattering procedure is a method of discovering designated options of two-dimensional types in quantum box idea and statistical physics (such because the sine-Gordon equation or the quantum nonlinear Schrödinger equation). This creation to this significant and fascinating zone first bargains with the Bethe ansatz and calculation of actual amounts.
One of many problems in an introductory e-book is to speak a feeling of function. basically too simply to the newbie does the e-book develop into a series of definitions, suggestions, and effects which look little greater than curiousities top nowhere specifically. during this publication i've got attempted to beat this challenge via making my significant goal the decision of all attainable teams of orders 1 to fifteen, including a few learn in their constitution.
This ebook introduces the factorization procedure in quantum mechanics at a complicated point, with the purpose of placing mathematical and actual strategies and strategies just like the factorization strategy, Lie algebras, matrix components and quantum keep an eye on on the reader’s disposal. For this function, the textual content presents a complete description of the factorization technique and its broad purposes in quantum mechanics which enhances the conventional assurance present in quantum mechanics textbooks.
- Quantentheorie 2: Quantisierung und Symmetrien physikalischer Systeme Relativistische Quantentheorie (Springer-Lehrbuch) (German Edition)
- The Quantum Theory of Motion
- The Quantum Handshake: Entanglement, Nonlocality and Transactions
- A Short Course in Quantum Information Theory: An Approach From Theoretical Physics (Lecture Notes in Physics)
- Boundary Values and Convolution in Ultradistribution Spaces (Series on Analysis, Applications and Computation ? Vol. 1)
- Are Quanta Real?: A Galilean Dialogue (A Midland Book)
Extra resources for Algebraic Approach to Simple Quantum Systems: With Applications to Perturbation Theory
These results will be useful later for the representation theory of so( 4). In the final section an alternate derivation of the matrix representation of a vector operator is given using some of the more advanced aspects of angular momentum theory based on the Wigner-Eckart theorem. This section is not essential for the understanding of later chapters. 2) The Casimir operator does not belong to so(3) since it is not a linear combination of the generators2. 3) lThe word "unirrep" refers to representations of the Lie group by unitary matrices or operators but it is common to also use it to refer to representations of the Lie algebra.
4 Realizations of so(2,1) It is not as straightforward to obtain realizations of so(2,1) as it is for so(3). Given the correspondence principle it is clear how to extend the classical orbital angular momentum to its quantum mechanical counterpart in order to obtain a realization in the coordinate representation for the generators of so(3). However there is no similar classical analogue in the coordinate representation for the generators of so(2,1). Since our goal is to use so(2,1) as a spectrum generating algebra for simple quantum systems such as the hydrogen atom and the harmonic oscillator, we look for realizations which can be used to express the hamiltonians for these systems in terms of the generators Tk.
Finally some useful vector identities involving L are r·L = L·r = 0, p·L = L·p= 0, p X L = r l - p(r. 35) P = 2ip. 5. 31) illustrates another useful rule: since r X r = O. This result also follows from the general rule: If A = L,jk ajk8jk is such that ajk is antisymmetric in j and k and 8jk is symmetric in j and k, then A = O. We can conclude that r • L = 0 since fjkl is antisymmetric in j and k but is symmetric in j and k. 1 Prove that if A = L,jk ajk8jk is such that ajk is antisymmetric in j and k and 8jk is symmetric in j and k, then A = O.