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Spinning Quantum System in an External Magnetic Field

  • Arno Bohm
  • Ali Mostafazadeh
  • Hiroyasu Koizumi
  • Qian Niu
  • Joseph Zwanziger
Part of the Texts and Monographs in Physics book series (TMP)

Abstract

In this chapter we will discuss in detail a quantum particle with magnetic moment m = µ B g J in an external magnetic field B(t) = (math) whose direction (math) is changing periodically. In particular we will consider the case in which the direction of the magnetic field precesses around a fixed axis which we take as the 3-axis (z-axis) of our (laboratory) coordinate frame in space (ℝ3). If the direction rotates slowly (“adiabatically”) this system provides an application of the general ideas developed in Chap. 2. The Schrödinger equation for a magnetic moment in a precessing magnetic field has been solved exactly in [216]. Therefore we need not restrict ourselves to the adiabatic approximation and will obtain the non-adiabatic geometric phase. The latter is also known as the Aharonov-Anandan phase [7, 9] for their pioneering work. With the help of this example we will then introduce in Sect. 3.5 the non-adiabatic geometric phase for a general cyclic evolution.

Keywords

State Vector Geometric Phase North Pole Magnetic Monopole Adiabatic Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Arno Bohm
    • 1
  • Ali Mostafazadeh
    • 2
  • Hiroyasu Koizumi
    • 3
  • Qian Niu
    • 1
  • Joseph Zwanziger
    • 4
  1. 1.Physics DepartmentUniversity of Texas at AustinAustinUSA
  2. 2.Department of MathematicsKoç UniversityIstanbulTurkey
  3. 3.Faculty of ScienceHimeji Institute of TechnologyHyogoJapan
  4. 4.Department of ChemistryIndiana UniversityBloomingtonUSA

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