| 紀錄類型: |
書目-電子資源
: 單行本
|
| 副題名: |
with extensions to many-body systems and integrable PDEs |
| 作者: |
OlshaniiM., |
| 出版地: |
Singapore |
| 出版者: |
World Scientific Pub. Co; |
| 出版年: |
c2014 |
| 面頁冊數: |
1 online resource (xviii, 151 p.)ill. : |
| 標題: |
Quantum theory - |
| 標題: |
Many-body problem - |
| 標題: |
Differential equations, Partial - |
| 電子資源: |
http://www.worldscientific.com/worldscibooks/10.1142/8811#t=toc |
| 附註: |
Include indexes |
| 摘要註: |
Dimensional and order-of-magnitude 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 three-line-long estimate for the ionization energy of atoms uniformly valid across the whole periodic table. The piece de resistance 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 Korteweg-de Vries equation and an expression for the oscillation period of a nonlinear Schrodinger breather as a function of its width |
| ISBN: |
9789814508476electronic bk. |
| ISBN: |
9814508470electronic bk. |
| 內容註: |
1. Ground state energy of a hybrid harmonic-quartic oscillator: a case study. 1.1. Solved problems -- 2. Bohr-Sommerfeld 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. Semi-classical 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 Hellmann-Feynman 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 |