Author 
Olshanii, M. (Maxim),

Subject 
Quantum theory.


Manybody problem.


Differential equations, Partial.

Alt Name 
World Scientific (Firm),

Description 
1 online resource (xviii, 151 pages) : illustrations 

polychrome rdacc http://rdaregistry.info/termList/RDAColourContent/1003 
Note 
Includes indexes. 
Contents 
1. Ground state energy of a hybrid harmonicquartic oscillator: a case study. 1.1. Solved problems  2. BohrSommerfeld quantization. 2.1. Solved problems. 2.2. Problems without provided solutions. 2.3. Background. 2.4. Problems linked to the "background"  3. "Halved" harmonic oscillator: a case study. 3.1. Solved problems  4. Semiclassical matrix elements of observables and perturbation theory. 4.1. Solved problems. 4.2. Problems without provided solutions. 4.3. Background  5. Variational problems. 5.1. Solved problems. 5.2. Problems without provided solutions. 5.3. Background. 5.4. Problems linked to the "background"  6. Gravitational well: a case study. 6.1. Solved problems  7. Miscellaneous. 7.1. Solved problems  8. The HellmannFeynman theorem. 8.1. Solved problems. 8.2. Problems without provided solutions. 8.3. Background  9. Local density approximation theories. 9.1. Solved problems. 9.2. Problems without provided solutions  10. Integrable partial differential equations. 10.1. Solved problems. 10.2. Problems without provided solutions. 
Summary 
Dimensional and orderofmagnitude estimates are practiced by almost everybody but taught almost nowhere. When physics students engage in their first theoretical research project, they soon learn that exactly solvable problems belong only to textbooks, that numerical models are long and resource consuming, and that "something else" is needed to quickly gain insight into the system they are going to study. Qualitative methods are this "something else", but typically, students have never heard of them before. The aim of this book is to teach the craft of qualitative analysis using a set of problems, some with solutions and some without, in advanced undergraduate and beginning graduate quantum mechanics. Examples include a dimensional analysis solution for the spectrum of a quartic oscillator, simple WKB formulas for the matrix elements of a coordinate in a gravitational well, and a threelinelong estimate for the ionization energy of atoms uniformly valid across the whole periodic table. The pièce de résistance in the collection is a series of dimensional analysis questions in integrable nonlinear partial differential equations with no dimensions existing a priori. Solved problems include the relationship between the size and the speed of solitons of the Kortewegde Vries equation and an expression for the oscillation period of a nonlinear Schrödinger breather as a function of its width. 
Note 
Print version record. 
ISBN 
9789814508476 (electronic bk.) 

9814508470 (electronic bk.) 

9789814508469 
OCLC # 
860388605 
Additional Format 
Print version: Olshanii, M. (Maxim). Backoftheenvelope quantum mechanics. Singapore ; Hackensack, N.J. : World Scientific Pub. Co., ©2014 9789814508469 
