Lectures On Quantum Mechanics - Volume 3: Perturbed Evolution

Lectures On Quantum Mechanics - Volume 3: Perturbed Evolution

by Berthold-georg Englert
ISBN-10:
9812569758
ISBN-13:
9789812569752
Pub. Date:
05/19/2006
Publisher:
World Scientific Publishing Company, Incorporated
ISBN-10:
9812569758
ISBN-13:
9789812569752
Pub. Date:
05/19/2006
Publisher:
World Scientific Publishing Company, Incorporated
Lectures On Quantum Mechanics - Volume 3: Perturbed Evolution

Lectures On Quantum Mechanics - Volume 3: Perturbed Evolution

by Berthold-georg Englert

Paperback

$45.0
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Overview

Note: The three volumes are not sequential but rather independent of each other and largely self-contained.Basic Matters is a first introduction to quantum mechanics that does not assume any prior knowledge of the subject. The emphasis is on the general structure as the necessary foundation of any understanding. Starting from the simplest quantum phenomenon, the Stern-Gerlach experiment with its choice between two discrete outcomes, and ending with one-dimensional continuous systems, the physical concepts and notions as well as the mathematical formalism of quantum mechanics are developed in successive, manageable steps. The presentation is modern inasmuch as the natural language of the trade - Dirac's kets and bras and so on - is introduced early, and the temporal evolution is dealt with in a picture-free manner, with Schrödinger's and Heisenberg's equations of motion side by side and on equal footing.The reader of Simple Systems is not expected to be familiar with the material in Basic Matters, but should have the minimal knowledge of a standard brief introduction to quantum mechanics with its typical emphasis on one-dimensional position wave functions. The step to Dirac's more abstract and much more powerful formalism is taken immediately, followed by reviews of quantum kinematics and quantum dynamics. The important standard examples (force-free motion, constant force, harmonic oscillator, hydrogen-like atoms) are then treated in considerable detail, whereby a nonstandard perspective is offered wherever it is deemed feasible and useful. A final chapter is devoted to approximation methods, from the Hellmann-Feynman theorem to the WKB quantization rule.Perturbed Evolution has a closer link to Simple Systems than that volume has to Basic Matters, but any reader familiar with the subject matter of a solid introduction to quantum mechanics - such as Dirac's formalism of kets and bras, Schrödinger's and Heisenberg's equations of motion, and the standard examples that can be treated exactly, with harmonic oscillators and hydrogen-like atoms among them - can cope with the somewhat advanced material of this volume. The basics of kinematics and dynamics are reviewed at the outset, including discussions of Bohr's principle of complementarity and Schwinger's quantum action principle. The Born series, the Lippmann-Schwinger equation, and Fermi's golden rule are recurring themes in the treatment of the central subject matter - the evolution in the presence of perturbing interactions for which there are no exact solutions as one has them for the standard examples in Simple Systems. The scattering by a localized potential is regarded as a perturbed evolution of a particular kind and is dealt with accordingly. The unique features of the scattering of indistinguishable quantum objects illustrate the nonclassical properties of bosons and fermions and prepare the groundwork for a discussion of multi-electron atoms.

Product Details

ISBN-13: 9789812569752
Publisher: World Scientific Publishing Company, Incorporated
Publication date: 05/19/2006
Series: Lectures on Quantum Mechanics
Pages: 212
Product dimensions: 6.00(w) x 8.90(h) x 0.50(d)

Table of Contents

Preface     vii
Basics of Kinematics and Dynamics     1
Brief review of basic kinematics     1
Bohr's principle of complementarity     7
Complementary observables     7
Algebraic completeness     13
Bohr's principle. Technical formulation     17
Composite degrees of freedom     17
The limit N to [infinity]. Symmetric case     19
The limit N to [infinity]. Asymmetric case     26
Bohr's principle. Quantum indeterminism     30
Brief review of basic dynamics     31
Equations of motion     31
Time transformation functions     33
Schwinger's quantum action principle     36
An example: Constant force     39
Insertion: Varying an exponential function     41
Time-independent Hamilton operator     43
Time-Dependent Perturbations     45
Born series     45
Scattering operator     48
Dyson series     50
Fermi's golden rule     52
Photon emission by a "two-level atom"     57
Golden-rule treatment     57
A more detailed treatment     60
An exact treatment     65
Driven two-level atom     68
Schrodinger equation     68
Resonant drive     71
Periodic drive     72
Very slow drive. Adiabatic evolution     74
Adiabatic population transfer     78
Equation of motion for the unitary evolution operator     81
Scattering     87
Probability density, probability current density     87
One-dimensional prelude: Forces scatter     91
Scattering by a localized potential     95
Golden-rule approximation     95
Example: Yukawa potential     100
Rutherford cross section as a limit     101
Lippmann-Schwinger equation     102
Born approximation     111
Transition operator     112
Optical theorem     114
Example of an exact solution     116
Partial waves     118
s-wave scattering     123
Angular Momentum     129
Spin     129
Addition of two angular momenta     134
Two spin-1/2 systems     137
Total angular momentum of an electron     138
External Magnetic Field     141
Electric charge in a magnetic field      141
Electron in a homogeneous magnetic field     148
Indistinguishable Particles     155
Indistinguishability     155
Bosons and fermions     157
Scattering of two indistinguishable particles     161
Two-electron atoms     165
Variational estimate for the ground state     165
Perturbative estimate for the first excited state     171
Self-consistent single-electron wave functions     173
A glimpse at many-electron atoms     175
Index     181
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