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-).

Phase State as a Cooper-Pair Number: Phase Minimum Uncertainty State for Josephson Junction

2003 ◽  
Vol 17 (13) ◽  
pp. 2599-2608 ◽  
Author(s):  
Hong-Yi Fan
Keyword(s):  
Josephson Junction ◽  
Cooper Pair ◽  
Uncertainty Relation ◽  
Phase State ◽  
Phase Operator ◽  
Operator Formalism ◽  
Hamiltonian Model ◽  
Pair Number ◽  
Minimum Uncertainty ◽  
Phase Uncertainty

Based on Feynman's explanation that a Cooper pair is "a bound pair act as a Bose particle", we propose a bosonic phase operator formalism and a bosonic Hamiltonian model for Josephson junction. The Cooper pair number — phase uncertainty relation is thus established. The corresponding minimum uncertainty state is derived which turns out to be a phase state.

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

MINIMUM UNCERTAINTY RELATION OBEYED BY SWH PHASE OPERATOR IN TWO-MODE COHERENT STATE

1999 ◽  
Vol 13 (14) ◽  
pp. 463-469 ◽  
Author(s):  
FAN HONGYI ◽  
SUN ZHIHU
Keyword(s):  
Coherent State ◽  
Uncertainty Relation ◽  
Phase Measurement ◽  
Single Mode ◽  
Square Root ◽  
Phase Operator ◽  
Expectation Values ◽  
Measurement Scheme ◽  
Minimum Uncertainty ◽  
Root Operation

We study the minimum uncertainty relation obeyed by the phase operator [Formula: see text] in two-mode coherent state. The operator is suitable for Shapiro–Wagner heterodyne phase measurement scheme. It is due to the |ξ> representation (see Eq. (4)) that the difficulty brought by nonlinear square root operation in [Formula: see text] can be avoided in calculating miscellaneous expectation values. Just as the single-mode coherent state | z1> makes uncertainty relation, satisfied by S–G phase operator, minimum for large |z1|2, we show that |z1,z2> makes uncertainty relation obeyed by [Formula: see text] minimum when |z1|=|z2| is large enough. Some figures are plotted to support our conclusion.

EINSTEIN–PODOLSKY–ROSEN ENTANGLED STATE REPRESENTATION FOR ANGULAR-MOMENTUM AND RADIUS ENTANGLEMENT

2004 ◽  
Vol 18 (07) ◽  
pp. 1043-1053 ◽  
Author(s):  
HONG-YI FAN ◽  
JUN-HUA CHEN
Keyword(s):  
Angular Momentum ◽  
Physical System ◽  
Total Momentum ◽  
Entangled State ◽  
Quantum Mechanical ◽  
Entangled State Representation ◽  
State Representation ◽  
Common Eigenvector ◽  
Einstein Podolsky Rosen ◽  
The Common

By comparison with the Einstein–Podolsky–Rosen coordinate-momentum entangled state, which is the common eigenvector of two particles' relative coordinate and total momentum, we construct a new quantum mechanical entangled state representation, namely, the entangled state representation of angular-momentum and radius. A concrete physical system which can embody the new quantum entanglement is analyzed.

ANGULAR MOMENTUM-PHASE WIGNER OPERATOR FOR DESCRIBING ELECTRONS IN UNIFORM MAGNETIC FIELDS

2001 ◽  
Vol 15 (12n13) ◽  
pp. 407-414 ◽  
Author(s):  
HONGYI FAN
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Magnetic Fields ◽  
Wigner Function ◽  
Uniform Magnetic Field ◽  
Marginal Distributions ◽  
Wigner Operator

By introducing the angular momentum-phase Wigner operator both in <λ| representation and <l,r| representation, which are respectively the eigenstates of position and angular momentum of an electron in a uniform magnetic field, we establish the angular momentum-phase Wigner function whose marginal distributions are physically meaningful.

Interaction Hamiltonian fro Relative-Number-Phase of Ban's Phase Operator Formalism

1998 ◽  
Vol 12 (18) ◽  
pp. 715-718
Author(s):  
Hong-Yi Fan ◽  
Yi-Hua Wang
Keyword(s):  
Uncertainty Relation ◽  
Relative Number ◽  
Phase Operator ◽  
Operator Formalism ◽  
Phase Uncertainty ◽  
Phase Operators

Based on Ban's phase operator formalism, we introduce the interaction Hamiltonian for studying relative-number-phase uncertainty relation. The time evolutions for the relative-number and phase operators are also discussed.

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