X
feed icon rss

Ihre E-Mail wurde erfolgreich gesendet. Bitte prüfen Sie Ihren Maileingang.

Leider ist ein Fehler beim E-Mail-Versand aufgetreten. Bitte versuchen Sie es erneut.

Vorgang fortführen?

Exportieren
  • 1
    Online-Ressource
    Online-Ressource
    Quantum Hamilton-Jacobi Formalism (2022)
    Cham :Springer International Publishing :
    Details
    UID:
    almahu_9949372042902882
    Umfang: XV, 112 p. 13 illus., 3 illus. in color. , online resource.
    Ausgabe: 1st ed. 2022.
    ISBN: 9783031106248
    Serie: SpringerBriefs in Physics,
    Inhalt: This book describes the Hamilton-Jacobi formalism of quantum mechanics, which allows computation of eigenvalues of quantum mechanical potential problems without solving for the wave function. The examples presented include exotic potentials such as quasi-exactly solvable models and Lame an dassociated Lame potentials. A careful application of boundary conditions offers an insight into the nature of solutions of several potential models. Advanced undergraduates having knowledge of complex variables and quantum mechanics will find this as an interesting method to obtain the eigenvalues and eigen-functions. The discussion on complex zeros of the wave function gives intriguing new results which are relevant for advanced students and young researchers. Moreover, a few open problems in research are discussed as well, which pose a challenge to the mathematically oriented readers.
    Anmerkung: The Quantum Hamilton Jacobi Formalism. - Exactly Solvable Models -- New Results on Singularities of QMF -- Rational Shape Invariant Extensions and Exceptional Polynomials -- QHJ in the Context of Other Related Work.
    In: Springer Nature eBook
    Weitere Ausg.: Printed edition: ISBN 9783031106231
    Weitere Ausg.: Printed edition: ISBN 9783031106255
    Sprache: Englisch
    DOI: 10.1007/978-3-031-10624-8
    URL: https://doi.org/10.1007/978-3-031-10624-8
    URL: Volltext  (URL des Erstveröffentlichers)
    URL: lizenzpflichtig
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
    Online-Ressource
    Online Zugang
    Open Access Wunsch
    HU Berlin
    UB Potsdam
    TH Brandenburg
  • 2
    Online-Ressource
    Online-Ressource
    Quantum Hamilton-Jacobi formalism / (2022)
    Cham, Switzerland :Springer,
    Details
    UID:
    edoccha_9960901281002883
    Umfang: 1 online resource (122 pages)
    ISBN: 3-031-10624-5
    Serie: SpringerBriefs in Physics
    Anmerkung: Intro -- Preface -- Acknowledgements -- Contents -- Acronyms -- 1 Quantum Hamilton-Jacobi Formalism -- 1.1 Introduction -- 1.2 Quantum Hamilton-Jacobi Formalism -- 1.2.1 Working in the Complex Plane -- 1.2.2 Boundary Condition -- 1.2.3 Exact Quantization Condition -- 1.3 Plan of the Book -- References -- 2 Mathematical Preliminaries -- 2.1 Introduction -- 2.2 Results from Theory of Complex Variables -- 2.2.1 Laurent Expansion -- 2.2.2 Liuoville Theorem -- 2.2.3 Meromorphic Function -- 2.3 Results from Theory of Differential Equations -- 2.3.1 Solutions of Riccati Equation -- 2.3.2 Singular Points of Solution of Riccati Equation -- 2.3.3 Real and Complex Zeros of the Wave Function -- 2.3.4 Riccati Equation-Some General Results -- 2.3.5 Reduction to a Second-Order Linear Differential Equation -- 2.3.6 Most General Solution from Given Solution(s) -- 2.4 Some Frequently Used Results and Examples -- 2.4.1 Residue of QMF at a Moving Pole -- 2.4.2 Evaluating Action Integral -- 2.5 Harmonic Oscillator-Method-I -- 2.5.1 Behaviour of p Subscript clpcl for Large StartAbsoluteValue x EndAbsoluteValue|x| -- 2.5.2 Classical Momentum in the Complex Plane -- 2.5.3 Boundary Condition on QMF -- 2.5.4 Energy Eigenvalues -- 2.6 Harmonic Oscillator-Method-II -- 2.6.1 Using Square Integrability -- 2.6.2 General Form of QMF -- 2.6.3 Energy Eigenvalues -- 2.6.4 Energy Eigenfunctions -- References -- 3 Exactly Solvable Models -- 3.1 Introduction -- 3.2 Change of Variable -- 3.3 Morse Oscillator -- 3.4 Radial Oscillator -- 3.5 Particle in a Box -- 3.6 Exactness of SWKB Approximation -- 3.7 Concluding Remarks -- References -- 4 Exotic Potentials -- 4.1 Introduction -- 4.2 A Periodic Potential -- 4.3 A Potential with Two Phases of SUSY -- 4.3.1 QHJ Solution of Scarf-I Potential -- 4.3.2 Change of Variable -- 4.3.3 Meromorphic Form of the QMF chiχ. , 4.3.4 Computation of the Residues Using QHJ -- 4.3.5 Leacock-Padgett Boundary Condition -- 4.4 Quasi-Exactly Solvable Models -- 4.4.1 Introduction to QES Models -- 4.4.2 A List of QES Potentials -- 4.4.3 QHJ Analysis of Sextic Oscillator -- 4.4.4 The Residue at Infinity -- 4.4.5 Form of the QMF and Wave Function -- 4.4.6 Properties of the Solutions -- 4.5 Band Edges for a Periodic Potential -- 4.5.1 Explicit Solution for j equals 2j=2 -- 4.6 A QES Periodic Potential -- 4.7 Some Observations -- References -- 5 Rational Extensions -- 5.1 Introduction -- 5.2 About ES Potentials and Orthogonal Polynomial Connection -- 5.3 Exceptional Orthogonal Polynomials -- 5.4 Extended Potentials -- 5.5 Supersymmetric Quantum Mechanics -- 5.6 Shape Invariance -- 5.7 Construction of New ES Models -- 5.7.1 Isospectral Deformation -- 5.7.2 Isospectral Shift Deformation -- 5.7.3 ISD and Shape Invariant Extensions -- 5.8 Radial Oscillator and Its Shape Invariant Extensions -- 5.9 Further Observations -- References -- 6 Complex Potentials and Optical Systems -- 6.1 Introduction -- 6.2 Complex script upper P script upper TmathcalPmathcalT-Symmetric Potentials -- 6.2.1 The Complex Scarf-II Potential -- 6.2.2 Variation of Parameters and Energy Spectrum -- 6.3 SUSY, script upper P script upper TmathcalPmathcalT-Symmetry and Optical Systems -- 6.4 Complex Scarf-II Potential: script upper P script upper TmathcalPmathcalT Symmetry and Supersymmetry -- 6.4.1 Broken and Unbroken Phases of script upper P script upper TmathcalPmathcalT-Symmetry -- 6.4.2 Unbroken script upper P script upper TmathcalPmathcalT and Broken SUSY Phase -- 6.4.3 Broken script upper P script upper TmathcalPmathcalT-Symmetric Phase -- References -- 7 Beyond One Dimension -- 7.1 Introduction -- 7.2 Classification of ES and QES Models -- 7.3 Open Questions and Concluding Remarks -- References -- Index.
    Weitere Ausg.: Print version: Kapoor, A. K. Quantum Hamilton-Jacobi Formalism Cham : Springer International Publishing AG,c2022 ISBN 9783031106231
    Sprache: Englisch
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
    Online-Ressource
    Charité
  • 3
    Online-Ressource
    Online-Ressource
    Quantum Hamilton-Jacobi formalism / (2022)
    Cham, Switzerland :Springer,
    Details
    UID:
    almafu_9960901281002883
    Umfang: 1 online resource (122 pages)
    ISBN: 3-031-10624-5
    Serie: SpringerBriefs in Physics
    Anmerkung: Intro -- Preface -- Acknowledgements -- Contents -- Acronyms -- 1 Quantum Hamilton-Jacobi Formalism -- 1.1 Introduction -- 1.2 Quantum Hamilton-Jacobi Formalism -- 1.2.1 Working in the Complex Plane -- 1.2.2 Boundary Condition -- 1.2.3 Exact Quantization Condition -- 1.3 Plan of the Book -- References -- 2 Mathematical Preliminaries -- 2.1 Introduction -- 2.2 Results from Theory of Complex Variables -- 2.2.1 Laurent Expansion -- 2.2.2 Liuoville Theorem -- 2.2.3 Meromorphic Function -- 2.3 Results from Theory of Differential Equations -- 2.3.1 Solutions of Riccati Equation -- 2.3.2 Singular Points of Solution of Riccati Equation -- 2.3.3 Real and Complex Zeros of the Wave Function -- 2.3.4 Riccati Equation-Some General Results -- 2.3.5 Reduction to a Second-Order Linear Differential Equation -- 2.3.6 Most General Solution from Given Solution(s) -- 2.4 Some Frequently Used Results and Examples -- 2.4.1 Residue of QMF at a Moving Pole -- 2.4.2 Evaluating Action Integral -- 2.5 Harmonic Oscillator-Method-I -- 2.5.1 Behaviour of p Subscript clpcl for Large StartAbsoluteValue x EndAbsoluteValue|x| -- 2.5.2 Classical Momentum in the Complex Plane -- 2.5.3 Boundary Condition on QMF -- 2.5.4 Energy Eigenvalues -- 2.6 Harmonic Oscillator-Method-II -- 2.6.1 Using Square Integrability -- 2.6.2 General Form of QMF -- 2.6.3 Energy Eigenvalues -- 2.6.4 Energy Eigenfunctions -- References -- 3 Exactly Solvable Models -- 3.1 Introduction -- 3.2 Change of Variable -- 3.3 Morse Oscillator -- 3.4 Radial Oscillator -- 3.5 Particle in a Box -- 3.6 Exactness of SWKB Approximation -- 3.7 Concluding Remarks -- References -- 4 Exotic Potentials -- 4.1 Introduction -- 4.2 A Periodic Potential -- 4.3 A Potential with Two Phases of SUSY -- 4.3.1 QHJ Solution of Scarf-I Potential -- 4.3.2 Change of Variable -- 4.3.3 Meromorphic Form of the QMF chiχ. , 4.3.4 Computation of the Residues Using QHJ -- 4.3.5 Leacock-Padgett Boundary Condition -- 4.4 Quasi-Exactly Solvable Models -- 4.4.1 Introduction to QES Models -- 4.4.2 A List of QES Potentials -- 4.4.3 QHJ Analysis of Sextic Oscillator -- 4.4.4 The Residue at Infinity -- 4.4.5 Form of the QMF and Wave Function -- 4.4.6 Properties of the Solutions -- 4.5 Band Edges for a Periodic Potential -- 4.5.1 Explicit Solution for j equals 2j=2 -- 4.6 A QES Periodic Potential -- 4.7 Some Observations -- References -- 5 Rational Extensions -- 5.1 Introduction -- 5.2 About ES Potentials and Orthogonal Polynomial Connection -- 5.3 Exceptional Orthogonal Polynomials -- 5.4 Extended Potentials -- 5.5 Supersymmetric Quantum Mechanics -- 5.6 Shape Invariance -- 5.7 Construction of New ES Models -- 5.7.1 Isospectral Deformation -- 5.7.2 Isospectral Shift Deformation -- 5.7.3 ISD and Shape Invariant Extensions -- 5.8 Radial Oscillator and Its Shape Invariant Extensions -- 5.9 Further Observations -- References -- 6 Complex Potentials and Optical Systems -- 6.1 Introduction -- 6.2 Complex script upper P script upper TmathcalPmathcalT-Symmetric Potentials -- 6.2.1 The Complex Scarf-II Potential -- 6.2.2 Variation of Parameters and Energy Spectrum -- 6.3 SUSY, script upper P script upper TmathcalPmathcalT-Symmetry and Optical Systems -- 6.4 Complex Scarf-II Potential: script upper P script upper TmathcalPmathcalT Symmetry and Supersymmetry -- 6.4.1 Broken and Unbroken Phases of script upper P script upper TmathcalPmathcalT-Symmetry -- 6.4.2 Unbroken script upper P script upper TmathcalPmathcalT and Broken SUSY Phase -- 6.4.3 Broken script upper P script upper TmathcalPmathcalT-Symmetric Phase -- References -- 7 Beyond One Dimension -- 7.1 Introduction -- 7.2 Classification of ES and QES Models -- 7.3 Open Questions and Concluding Remarks -- References -- Index.
    Weitere Ausg.: Print version: Kapoor, A. K. Quantum Hamilton-Jacobi Formalism Cham : Springer International Publishing AG,c2022 ISBN 9783031106231
    Sprache: Englisch
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
    Online-Ressource
    Charité
Nichts oder nicht das Richtige gefunden? Bitte überprüfen Sie Ihre Suchanfrage oder benutzen Sie den Fernleihindex.
Meinten Sie 9783031065231?
Meinten Sie 9783030116231?
Meinten Sie 9783031100239?
Schließen ⊗
Diese Webseite nutzt Cookies und das Analyse-Tool Matomo. Weitere Informationen finden Sie auf den KOBV Seiten zum Datenschutz