The Resource Back-of-the-envelope quantum mechanics : with extensions to many-body systems and integrable PDEs, Maxim Olshanii, University of Massachusetts Boston, USA

Back-of-the-envelope quantum mechanics : with extensions to many-body systems and integrable PDEs, Maxim Olshanii, University of Massachusetts Boston, USA

Label
Back-of-the-envelope quantum mechanics : with extensions to many-body systems and integrable PDEs
Title
Back-of-the-envelope quantum mechanics
Title remainder
with extensions to many-body systems and integrable PDEs
Statement of responsibility
Maxim Olshanii, University of Massachusetts Boston, USA
Creator
Subject
Genre
Language
  • eng
  • eng
Summary
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 p
Cataloging source
MiAaPQ
http://library.link/vocab/creatorName
Olshanii, M.
Dewey number
530.12
Illustrations
  • illustrations
  • charts
Index
index present
Language note
English
LC call number
QC174.12
LC item number
.O47 2014
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/subjectName
Quantum theory
Label
Back-of-the-envelope quantum mechanics : with extensions to many-body systems and integrable PDEs, Maxim Olshanii, University of Massachusetts Boston, USA
Instantiates
Publication
Copyright
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Preface; Contents; 1. Ground State Energy of a Hybrid Harmonic-Quartic Oscillator: A Case Study; 1.1 Solved problems; 1.1.1 Dimensional analysis and why it fails in this case; 1.1.1.1 Side comment: dimensional analysis and approximations; 1.1.1.2 Side comment: how to recast input equations in a dimensionless form; 1.1.2 Dimensional analysis: the harmonic oscillator alone; 1.1.3 Order-of-magnitude estimate: full solution; 1.1.3.1 Order-of-magnitude estimates vis-a-vis dimensional analysis; 1.1.3.2 Harmonic vs. quartic regimes; 1.1.3.3 The harmonic oscillator alone
  • 1.1.3.4 The quartic oscillator alone1.1.3.5 The boundary between the regimes and the final result; 1.1.4 An afterthought: boundary between regimes from dimensional considerations; 1.1.5 A Gaussian variational solution; 2. Bohr-Sommerfeld Quantization; 2.1 Solved problems; 2.1.1 A semi-classical analysis of the spectrum of a harmonic oscillator: the exact solution, an order-of-magnitude estimate, and dimensional analysis; 2.1.2 WKB treatment of a "straightened" harmonic oscillator; 2.1.3 Ground state energy in power-law potentials; 2.1.4 Spectrum of power-law potentials
  • 2.1.5 The number of bound states of a diatomic molecule2.1.6 Coulomb problem at zero angular momentum; 2.1.7 Quantization of angular momentum from WKB; 2.1.8 From WKB quantization of 4D angular momentum to quantization of the Coulomb problem; 2.2 Problems without provided solutions; 2.2.1 Size of a neutral meson in Schwinger's toy model of quark confinement; 2.2.2 Bohr-Sommerfeld quantization for periodic boundary conditions; 2.2.3 Ground state energy of multi-dimensional powerlaw potentials; 2.2.4 Ground state energy of a logarithmic potential; 2.2.5 Spectrum of a logarithmic potential
  • 2.2.6 1D box as a limit of power-law potentials2.2.7 Spin-1/2 in the field of a wire; 2.2.8 Dimensional analysis of the time-dependent Schro-dinger equation for a hybrid harmonicquartic oscillator; 2.3 Background; 2.3.1 Bohr-Sommerfeld quantization; 2.3.2 Multi-dimensional WKB; 2.4 Problems linked to the "Background"; 2.4.1 Bohr-Sommerfeld quantization for one soft turning point and a hard wall; 2.4.2 Bohr-Sommerfeld quantization for two hard walls; 3. "Halved" Harmonic Oscillator: A Case Study; Introduction; 3.1 Solved Problems; 3.1.1 Dimensional analysis; 3.1.2 Order-of-magnitude estimate
  • 3.1.3 Another order-of-magnitude estimate3.1.4 Straightforward WKB; 3.1.5 Exact solution; 4. Semi-Classical Matrix Elements of Observables and Perturbation Theory; 4.1 Solved problems; 4.1.1 Quantum expectation value of x6 in a harmonic oscillator; 4.1.2 Expectation value of r2 for a circular Coulomb orbit; 4.1.3 WKB approximation for some integrals involving spherical harmonics; 4.1.4 Ground state wave function of a one dimensional box; 4.1.5 Eigenstates of the harmonic oscillator at the origin: how a factor of two can restore a quantum-classical correspondence
  • 4.1.6 Probability density distribution in a "straightened" harmonic oscillator
Dimensions
unknown
Extent
1 online resource (170 p.)
Form of item
online
Isbn
9789814508476
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2550000001160079
  • (EBL)1561246
  • (OCoLC)860388605
  • (SSID)ssj0001153164
  • (PQKBManifestationID)11682140
  • (PQKBTitleCode)TC0001153164
  • (PQKBWorkID)11151048
  • (PQKB)10219428
  • (MiAaPQ)EBC1561246
  • (WSP)00008811
  • (EXLCZ)992550000001160079
Label
Back-of-the-envelope quantum mechanics : with extensions to many-body systems and integrable PDEs, Maxim Olshanii, University of Massachusetts Boston, USA
Publication
Copyright
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Preface; Contents; 1. Ground State Energy of a Hybrid Harmonic-Quartic Oscillator: A Case Study; 1.1 Solved problems; 1.1.1 Dimensional analysis and why it fails in this case; 1.1.1.1 Side comment: dimensional analysis and approximations; 1.1.1.2 Side comment: how to recast input equations in a dimensionless form; 1.1.2 Dimensional analysis: the harmonic oscillator alone; 1.1.3 Order-of-magnitude estimate: full solution; 1.1.3.1 Order-of-magnitude estimates vis-a-vis dimensional analysis; 1.1.3.2 Harmonic vs. quartic regimes; 1.1.3.3 The harmonic oscillator alone
  • 1.1.3.4 The quartic oscillator alone1.1.3.5 The boundary between the regimes and the final result; 1.1.4 An afterthought: boundary between regimes from dimensional considerations; 1.1.5 A Gaussian variational solution; 2. Bohr-Sommerfeld Quantization; 2.1 Solved problems; 2.1.1 A semi-classical analysis of the spectrum of a harmonic oscillator: the exact solution, an order-of-magnitude estimate, and dimensional analysis; 2.1.2 WKB treatment of a "straightened" harmonic oscillator; 2.1.3 Ground state energy in power-law potentials; 2.1.4 Spectrum of power-law potentials
  • 2.1.5 The number of bound states of a diatomic molecule2.1.6 Coulomb problem at zero angular momentum; 2.1.7 Quantization of angular momentum from WKB; 2.1.8 From WKB quantization of 4D angular momentum to quantization of the Coulomb problem; 2.2 Problems without provided solutions; 2.2.1 Size of a neutral meson in Schwinger's toy model of quark confinement; 2.2.2 Bohr-Sommerfeld quantization for periodic boundary conditions; 2.2.3 Ground state energy of multi-dimensional powerlaw potentials; 2.2.4 Ground state energy of a logarithmic potential; 2.2.5 Spectrum of a logarithmic potential
  • 2.2.6 1D box as a limit of power-law potentials2.2.7 Spin-1/2 in the field of a wire; 2.2.8 Dimensional analysis of the time-dependent Schro-dinger equation for a hybrid harmonicquartic oscillator; 2.3 Background; 2.3.1 Bohr-Sommerfeld quantization; 2.3.2 Multi-dimensional WKB; 2.4 Problems linked to the "Background"; 2.4.1 Bohr-Sommerfeld quantization for one soft turning point and a hard wall; 2.4.2 Bohr-Sommerfeld quantization for two hard walls; 3. "Halved" Harmonic Oscillator: A Case Study; Introduction; 3.1 Solved Problems; 3.1.1 Dimensional analysis; 3.1.2 Order-of-magnitude estimate
  • 3.1.3 Another order-of-magnitude estimate3.1.4 Straightforward WKB; 3.1.5 Exact solution; 4. Semi-Classical Matrix Elements of Observables and Perturbation Theory; 4.1 Solved problems; 4.1.1 Quantum expectation value of x6 in a harmonic oscillator; 4.1.2 Expectation value of r2 for a circular Coulomb orbit; 4.1.3 WKB approximation for some integrals involving spherical harmonics; 4.1.4 Ground state wave function of a one dimensional box; 4.1.5 Eigenstates of the harmonic oscillator at the origin: how a factor of two can restore a quantum-classical correspondence
  • 4.1.6 Probability density distribution in a "straightened" harmonic oscillator
Dimensions
unknown
Extent
1 online resource (170 p.)
Form of item
online
Isbn
9789814508476
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2550000001160079
  • (EBL)1561246
  • (OCoLC)860388605
  • (SSID)ssj0001153164
  • (PQKBManifestationID)11682140
  • (PQKBTitleCode)TC0001153164
  • (PQKBWorkID)11151048
  • (PQKB)10219428
  • (MiAaPQ)EBC1561246
  • (WSP)00008811
  • (EXLCZ)992550000001160079

Library Locations

  • Albert D. Cohen Management LibraryBorrow it
    181 Freedman Crescent, Winnipeg, MB, R3T 5V4, CA
    49.807878 -97.129961
  • Architecture/Fine Arts LibraryBorrow it
    84 Curry Place, Winnipeg, MB, CA
    49.807716 -97.136226
  • Archives and Special CollectionsBorrow it
    25 Chancellors Circle (Elizabeth Dafoe Library), Room 330, Winnipeg, MB, R3T 2N2, CA
    49.809961 -97.131878
  • Bibliothèque Alfred-Monnin (Université de Saint-Boniface)Borrow it
    200, avenue de la Cathédrale, Local 2110, Winnipeg, MB, R2H 0H7, CA
    49.888861 -97.119735
  • Bill Larson Library (Grace Hospital)Borrow it
    300 Booth Drive, G-227, Winnipeg, MB, R3J 3M7, CA
    49.882400 -97.276436
  • Carolyn Sifton - Helene Fuld Library (St. Boniface General Hospital)Borrow it
    409 Tache Avenue, Winnipeg, MB, R2H 2A6, CA
    49.883388 -97.126050
  • Concordia Hospital LibraryBorrow it
    1095 Concordia Avenue, Winnipeg, MB, R2K 3S8, CA
    49.913252 -97.064683
  • Donald W. Craik Engineering LibraryBorrow it
    75B Chancellors Circle (Engineering Building E3), Room 361, Winnipeg, MB, R3T 2N2, CA
    49.809053 -97.133292
  • E.K. Williams Law LibraryBorrow it
    224 Dysart Road, Winnipeg, MB, R3T 5V4, CA
    49.811829 -97.131017
  • Eckhardt-Gramatté Music LibraryBorrow it
    136 Dafoe Road (Taché Arts Complex), Room 257, Winnipeg, MB, R3T 2N2, CA
    49.807964 -97.132222
  • Elizabeth Dafoe LibraryBorrow it
    25 Chancellors Circle, Winnipeg, MB, R3T 2N2, CA
    49.809961 -97.131878
  • Fr. H. Drake Library (St. Paul's College)Borrow it
    70 Dysart Road, Winnipeg, MB, R3T 2M6, CA
    49.810605 -97.138184
  • J.W. Crane Memorial Library (Deer Lodge Centre)Borrow it
    2109 Portage Avenue, Winnipeg, MB, R3J 0L3, CA
    49.878000 -97.235520
  • Libraries Annex (not open to the public; please see web page for details)Borrow it
    25 Chancellors Circle (in the Elizabeth Dafoe Library), Winnipeg, MB, R3T 2N2, CA
    49.809961 -97.131878
  • Neil John Maclean Health Sciences LibraryBorrow it
    727 McDermot Avenue (Brodie Centre), 200 Level, Winnipeg, MB, R3E 3P5, CA
    49.903563 -97.160554
  • Sciences and Technology LibraryBorrow it
    186 Dysart Road, Winnipeg, MB, R3T 2M8, CA
    49.811526 -97.133257
  • Seven Oaks General Hospital LibraryBorrow it
    2300 McPhillips Street, Winnipeg, MB, R2V 3M3, CA
    49.955177 -97.148865
  • Sister St. Odilon Library (Misericordia Health Centre)Borrow it
    99 Cornish Avenue, Winnipeg, MB, R3C 1A2, CA
    49.879592 -97.160425
  • St. John's College LibraryBorrow it
    92 Dysart Road, Winnipeg, MB, R3T 2M5, CA
    49.811242 -97.137156
  • Victoria General Hospital LibraryBorrow it
    2340 Pembina Highway, Winnipeg, MB, R3T 2E8, CA
    49.806755 -97.152739
  • William R Newman Library (Agriculture)Borrow it
    66 Dafoe Road, Winnipeg, MB, R3T 2R3, CA
    49.806936 -97.135525
Processing Feedback ...