Back-of-the-envelope quantum mechanics: with extensions to many-body systems and integrable PDEs
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2014
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Include indexes 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 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 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 Korteweg-de Vries equation and an expression for the oscillation period of a nonlinear Schrödinger breather as a function of its width |
| Beschreibung: | 1 Online-Ressource (xviii, 151 p.) |
| ISBN: | 9789814508469 9789814508476 9814508470 |
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| 500 | |a Include indexes | ||
| 500 | |a 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 | ||
| 500 | |a 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 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 Korteweg-de Vries equation and an expression for the oscillation period of a nonlinear Schrödinger breather as a function of its width | ||
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| 650 | 7 | |a Partielle Differentialgleichung |2 gnd | |
| 650 | 7 | |a Vielkörperproblem |2 gnd | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Quantum theory | |
| 650 | 4 | |a Many-body problem | |
| 650 | 4 | |a Differential equations, Partial | |
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Datensatz im Suchindex
| _version_ | 1804175515271036928 |
|---|---|
| any_adam_object | |
| author | Olshanii, M., (Maxim) |
| author_facet | Olshanii, M., (Maxim) |
| author_role | aut |
| author_sort | Olshanii, M., (Maxim) |
| author_variant | m m o mm mmo |
| building | Verbundindex |
| bvnumber | BV043103076 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)860388605 (DE-599)BVBBV043103076 |
| dewey-full | 530.12 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12 |
| dewey-search | 530.12 |
| dewey-sort | 3530.12 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
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| id | DE-604.BV043103076 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:17:31Z |
| institution | BVB |
| isbn | 9789814508469 9789814508476 9814508470 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028527267 |
| oclc_num | 860388605 |
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| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xviii, 151 p.) |
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| publishDate | 2014 |
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| spelling | Olshanii, M., (Maxim) Verfasser aut Back-of-the-envelope quantum mechanics with extensions to many-body systems and integrable PDEs Maxim Olshanii Singapore World Scientific Pub. Co. c2014 1 Online-Ressource (xviii, 151 p.) txt rdacontent c rdamedia cr rdacarrier Include indexes 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 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 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 Korteweg-de Vries equation and an expression for the oscillation period of a nonlinear Schrödinger breather as a function of its width SCIENCE / Energy bisacsh SCIENCE / Mechanics / General bisacsh SCIENCE / Physics / General bisacsh Quantenmechanik gnd Partielle Differentialgleichung gnd Vielkörperproblem gnd Quantentheorie Quantum theory Many-body problem Differential equations, Partial Näherungsverfahren (DE-588)4206467-3 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s Näherungsverfahren (DE-588)4206467-3 s 1\p DE-604 World Scientific (Firm) Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=661916 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Olshanii, M., (Maxim) Back-of-the-envelope quantum mechanics with extensions to many-body systems and integrable PDEs SCIENCE / Energy bisacsh SCIENCE / Mechanics / General bisacsh SCIENCE / Physics / General bisacsh Quantenmechanik gnd Partielle Differentialgleichung gnd Vielkörperproblem gnd Quantentheorie Quantum theory Many-body problem Differential equations, Partial Näherungsverfahren (DE-588)4206467-3 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4206467-3 (DE-588)4047989-4 |
| title | Back-of-the-envelope quantum mechanics with extensions to many-body systems and integrable PDEs |
| title_auth | Back-of-the-envelope quantum mechanics with extensions to many-body systems and integrable PDEs |
| title_exact_search | Back-of-the-envelope quantum mechanics with extensions to many-body systems and integrable PDEs |
| title_full | Back-of-the-envelope quantum mechanics with extensions to many-body systems and integrable PDEs Maxim Olshanii |
| title_fullStr | Back-of-the-envelope quantum mechanics with extensions to many-body systems and integrable PDEs Maxim Olshanii |
| title_full_unstemmed | Back-of-the-envelope quantum mechanics with extensions to many-body systems and integrable PDEs Maxim Olshanii |
| title_short | Back-of-the-envelope quantum mechanics |
| title_sort | back of the envelope quantum mechanics with extensions to many body systems and integrable pdes |
| title_sub | with extensions to many-body systems and integrable PDEs |
| topic | SCIENCE / Energy bisacsh SCIENCE / Mechanics / General bisacsh SCIENCE / Physics / General bisacsh Quantenmechanik gnd Partielle Differentialgleichung gnd Vielkörperproblem gnd Quantentheorie Quantum theory Many-body problem Differential equations, Partial Näherungsverfahren (DE-588)4206467-3 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | SCIENCE / Energy SCIENCE / Mechanics / General SCIENCE / Physics / General Quantenmechanik Partielle Differentialgleichung Vielkörperproblem Quantentheorie Quantum theory Many-body problem Differential equations, Partial Näherungsverfahren |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=661916 |
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