# Mathematical Methods in Physics: Distributions, Hilbert Space Operators, Variational Methods, and Applications in Quantum Physics

The second edition of this textbook presents the basic mathematical knowledge and skills that are needed for courses on modern theoretical physics, such as those on quantum mechanics, classical and quantum field theory, and related areas. The authors stress that learning mathematical physics is not a passive process and include numerous detailed proofs, examples, and over 200 exercises, as well as hints linking mathematical concepts and results to the relevant physical concepts and theories. All of the material from the first edition has been updated, and five new chapters have been added on such topics as distributions, Hilbert space operators, and variational methods. The text is divided into three parts: - Part I: A brief introduction to Schwartz distribution theory. Elements from the theories of ultra distributions and Fourier hyperfunctions are given in addition to some deeper results for Schwartz distributions, thus providing a rather comprehensive introduction to the theory of generalized functions. Basic properties and methods for distributions are developed with applications to constant coefficient ODEs and PDEs. The relation between distributions and holomorphic functions is considered, as well as basic properties of Sobolev spaces. - Part II: Fundamental facts about Hilbert spaces. The basic theory of linear bounded and unbounded operators in Hilbert spaces and special classes of linear operators - compact, Hilbert-Schmidt, trace class, and Schroedinger operators, as needed in quantum physics and quantum information theory - are explored. This section also contains a detailed spectral analysis of all major classes of linear operators, including completeness of generalized eigenfunctions, as well as of completely positive mappings, in particular quantum operations. - Part III: Direct methods of the calculus of variations and their applications to boundary- and eigenvalue-problems for linear and nonlinear partial differential operators. The authors conclude with a discussion of the Hohenberg-Kohn variational principle. The appendices contain proofs of more general and deeper results, including completions, basic facts about metrizable Hausdorff locally convex topological vector spaces, Baire's fundamental results and their main consequences, and bilinear functionals. Mathematical Methods in Physics is aimed at a broad community of graduate students in mathematics, mathematical physics, quantum information theory, physics and engineering, as well as researchers in these disciplines. Expanded content and relevant updates will make this new edition a valuable resource for those working in these disciplines.

View more

Number of Pages: 598
Format(s): Hardback - ISBN: 9783319140445
Publication Date:
Listed in: General issues, Functional analysis & transforms, Optimization, Linear programming, Mathematical physics
Publishers: Birkhauser

Hardback

RRP: £99.00

Sale Price: £81.66

Save: £17.34 per copy!

£14.99

£12.99

## Deep Beauty: Understanding the Quantum World through Mathematical Innovation

Save £8.64 = £65.36

## Hamiltonian Mechanics of Gauge Systems

### By Lev V. Prokhorov

Save £31.94 = £54.06

## String Theory and Particle Physics: An Introduction to String Phenomenology

### By Luis E. Ibanez

Save £3.74 = £36.25

## Latest from the blog

### Fantastic new recipe book from Sabrina Ghayour 'Sirocco'

Sabrina Ghayour's long awaited second recipe book Sirocco is out this month and is a great follow up to Persianna. Read article

### Ten Great Bedtime Reads from The Great British Bookshop and Aspace

We have teamed up with Aspace (www.aspace.co.uk) who create beautiful room for Children to bring you 10 great bedtime reads for your little ones. Read article

## Breaking book world news

Posted 09/06/2016

### Literary Event Focus June-Sept 2016

Posted 23/02/2015

### Bath Literature Festival Judges deem Wolf Hall as 'outstanding novel of our time'

Posted 19/02/2015

## Latest from Twitter

• @TheGBBookshop - 2 years ago

Lottery funding for dementia reading project £2m pledged for Reading Agency scheme to pair readers with dementia sufferers

@TheGBBookshop - 2 years ago

Harry Potter and the Cursed Child has held on to the number one spot for a sixth week #HarryPotter #CursedChild @littlebrown @pottermore

• @TheGBBookshop - 2 years ago

@thebookseller @MartinaCole @Jeffrey_Archer @Foyles

@TheGBBookshop - 2 years ago

Frith wins inaugural Klaus Flugge Prize for illustration t.co/U9P08h4XMG

• @TheGBBookshop - 3 years ago

RT @Gue_de_Bost: #Dordogneholidaycottage available Sept tweet to book for more info

@TheGBBookshop - 3 years ago

The editor is just back from france @HomeAwayUK! t.co/IWutTER1x7