NEW REPRESENTATION FOR DESCRIBING LOWERING AND ASCENDING OF AN ELECTRON'S ANGULAR MOMENTUM IN A UNIFORM MAGNETIC FIELD

1999 ◽  
Vol 13 (08) ◽  
pp. 249-254 ◽  
Author(s):  
HONG-YI FAN ◽  
H. ZOU ◽  
YUE FAN
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Uniform Magnetic Field ◽  
Quantum Mechanical ◽  
Quantum Mechanical Representation ◽  
Lowering Operators

We construct a new quantum mechanical representation |l,r> for describing an electron's angular momentum in a uniform magnetic field, where l is the eigenvalue of the azimuthal angular momentum Lz and r is the orbit radius of the electron's motion. The ascending and lowering operators for |l,r>→|l± 1,r> are also obtained. Throughout our discussion the <λ| representation is fully employed (see Hong-Yi Fan and Yong Ren, Mod. Phys. Lett.B10, 523 (1996).

scholarly journals Is the Angular Momentum of an Electron Conserved in a Uniform Magnetic Field?

2014 ◽  
Vol 113 (24) ◽  
Author(s):  
Colin R. Greenshields ◽  
Robert L. Stamps ◽  
Sonja Franke-Arnold ◽  
Stephen M. Barnett
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Uniform Magnetic Field

scholarly journals Quantum mechanical grad-B drift velocity operator in a weakly non-uniform magnetic field

2016 ◽  
Vol 23 (2) ◽  
pp. 022104 ◽  
Author(s):  
Poh Kam Chan ◽  
Shun-ichi Oikawa ◽  
Wataru Kosaka
Keyword(s):  
Magnetic Field ◽  
Drift Velocity ◽  
Uniform Magnetic Field ◽  
Quantum Mechanical

scholarly journals Verallgemeinerte Boltzmann-Gleichung für mehratomige Gase

1967 ◽  
Vol 22 (12) ◽  
pp. 1871-1889 ◽  
Author(s):  
S. Hess
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Boltzmann Equation ◽  
Transport Equation ◽  
Internal State ◽  
Quantum Mechanical ◽  
Collision Term ◽  
Special Cases ◽  
Generalized Boltzmann Equation ◽  
Non Local

A generalized quantum mechanical Boltzmann equation is derived for the one particle distribution operator of a dilute gas consisting of molecules with arbitrary internal degrees of freedom. The effect of an external, time-independent potential on the scattering process is taken into account. The collision term of the transport equation contains the two-particle scattering operator T and its adjoint in a bilinear way and is non-local. The conservation equations for number of particles, energy, momentum and angular momentum as well as the H-theorem are deduced from the transport equation. One obtains the correct equilibrium distribution operator even in the presence of an external field (e. g. for particles with spin in a homogeneous magnetic field). Some special cases of the generalized Boltzmann equation are discussed treating position and momentum of a particle as classical variables but characterizing the internal state of a molecule by quantum mechanical observables. Using the local part of the collision term only and considering molecules with degenerate, but sufficiently separated internal energy levels one arrives at the Waldmann-Snider equation, which in turn comprises the Waldmann equation for particles with spin and the Wang Chang-Uhlenbeck equation. Special attention is drawn to the case of particles with spin in a magnetic field. Finally, for particles with spin, the local conservation equation for angular momentum, i.e. the Barnett effect (magnetization by rotation) and the antisymmetric part of the pressure tensor are derived from the generalized Boltzmann equation with non-local collision term.

MINIMUM UNCERTAINTY STATES FOR ANGULAR-MOMENTUM–PHASE UNCERTAINTY RELATION IN RADIUS–PHASE DESCRIPTION OF AN ELECTRON IN UNIFORM MAGNETIC FIELD

2000 ◽  
Vol 14 (07n08) ◽  
pp. 235-242 ◽  
Author(s):  
HONG-YI FAN
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Uniform Magnetic Field ◽  
Uncertainty Relation ◽  
Phase Operator ◽  
Common Eigenvector ◽  
Minimum Uncertainty ◽  
The Common ◽  
Phase Uncertainty

Based on the |λ> representation and the radius–phase description of an electron's orbit track in a uniform magnetic field, we introduce the phase operator and derive the minimum uncertainty states for the angular-momentum–phase uncertainty relation. The derivation makes full use of the newly constructed |l, r> representation which is the common eigenvector of the angular momentum Lz and the radius operator (K- - iΠ+)(K+ + iΠ-).

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