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  • 180pp. Published May 2017
  • Scientific Research Publishing, Inc.,USA.
  • Category: Biomedical & Life Sciences
  • ISBN: 978-1-61896-375-8
  • (Paperback) USD 89.00
  • ISBN: 978-1-61896-376-5
  • (E-Book) USD 29.00

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Home > Books > The Dynamics of Systems with Spin
The Dynamics of Systems with Spin
  • Description
  • E-Book
  • Author(s) Information

The incorporation of spin within classical mechanics suggests the following revision: the Euler equations, or the concept of a time-derivative operator relative to different reference frames, should be our new theoretical paradigm.

From here, the existence of formal developments valid both in classical and in quantum mechanics are explored through the analysis of topics such as: the dynamics of a particle with spin acted upon by a torque, the Thomas precession, the equations of evolution for spin, the concept of quantization, the anomalous Zeeman effect and the energy of the spin-orbit interaction.
The obtained results coincide for already-known concepts as well as those found within quantum theories. For example, when considering the evolution of particles with spin within magnetic fields, classical equations of motion present equivalent results as those derived using equations of evolution for expected quantum values.  This means that there are similarities supporting and justifying the point of view adopted in this book. 

The author hopes that the reader may benefit from and enjoy reading this text. For all whom read and enjoy reading this publication, he pass on the words Virgil used when talking about Lucretius, the author of De Rerum Natura, “Fortunate is he who is able to know the causes of things.”

Components of the Book:
  • Chapter 1: The classical spin or intrinsic angular momentum
    • 1.1. Introduction
  • Chapter 2: Euler’s equations
    • 2.1. Introduction
    • 2.2. Independent coordinates for a rigid body
    • 2.3. Coordinate systems fixed to a rigid body
    • 2.4. Orthogonal transformations
    • 2.5. A new definition for Euler’s theorem-additional hypotheses
    • 2.6. Conclusions
  • Chapter 3: The time derivative operator versus the reference frame
    • 3.1. Introduction
    • 3.2. Infinitesimal rotations
    • 3.3. Conclusions
  • Chapter 4: The dynamics of a system conserving kinetic energy, intrinsic angular momentum and helicity
    • 4.1. Introduction
    • 4.2. Conservation of kinetic energy
    • 4.3. Obtaining the equations of dynamics
    • 4.4. Equivalence between the conservation of energy and the conservation of helicity
    • 4.5. Lorentz-type forces and the conservation of helicity
    • 4.6. Conclusions
  • Chapter 5: The dynamics of a particle with spin
    • 5.1. Introduction
    • 5.2. A particle with spin in a “rotating/precessional” frame of reference and a gravitational field
    • 5.3. A particle with spin in a “rotating/precessional” frame of reference and an electric field
    • 5.4. Electrodynamics and gravitational dynamics
    • 5.5. The continuity equation
    • 5.6. Additional considerations
  • Chapter 6: The Thomas precession, the anomalous Zeeman effect and the spin-orbit interaction energy
    • 6.1. Introduction
    • 6.2. Concept development
    • 6.3. The anomalous Zeeman effect and spin-orbit coupling
    • 6.4. Quantum justification
    • 6.5. Conclusions
  • Chapter 7: Non-inertial frames of reference
    • 7.1. Introduction
    • 7.2. Rigid motion
    • 7.3. Transforming the velocity
    • 7.4. Transforming the acceleration
    • 7.5. Transforming Newton’s Law
  • Chapter 8: Equations of evolution of spin
    • 8.1. Introduction
    • 8.2. Proposal
    • 8.3. The classic solution
    • 8.4. A new method for resolving equations of evolution of spin
  • Chapter 9: Quantization and the calculation of the up-down transition energy
    • 9.1. Quantization
    • 9.2. Calculating energy variations in an up-down transition
  • Appendices
    • Appendix A. About Euler’s angles
    • Appendix B. Covariant relativistic formulas for one particle dynamics
    • Appendix C. Motion constants—another way to do the calculation
    • Appendix D. Energy conservation
    • Appendix E. Equations of evolution for quantum spin
    • Appendix F. The symmetrical spinning top
    • Appendix G. Trajectory calculations
    • Appendix H. Experimental research
    • Bibliography
Readership: Researchers, Postgraduate students, Graduate students, Undergraduate students, College/High School students
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