New Bosonic Operator Ordering Identities Gained by the Entangled State Representation and Two-Variable Hermite Polynomials

We find some new integration transformations in complex space, which plays the role of entangling or disentangling in quantum mechanics. Their applications in operator ordering are presented. We employ the entangled state representation and the method of integration within ordered product of operators (IWOP) to find them.

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ENTANGLED STATE REPRESENTATION FOR A PARTICLE ON A CIRCLE STUDIED IN TERMS OF BOSONIC OPERATOR REALIZATION OF ANGULAR MOMENTUM

Modern Physics Letters A ◽

10.1142/s021773230602010x ◽

2006 ◽

Vol 21 (27) ◽

pp. 2079-2085 ◽

Cited By ~ 2

Author(s):

HONG-YI FAN

Keyword(s):

Quantum Mechanics ◽

Angular Momentum ◽

Entangled States ◽

Entangled State ◽

Entangled State Representation ◽

Phase Operator ◽

State Representation ◽

New Formalism ◽

Bosonic Operator ◽

Operator Realization

By introducing the bosonic operator realization of angular momentum, we establish the entangled state representation for describing quantum mechanics of a particle on a circle. The phase operator, the angular momentum eigenstates, the lowering and ascending operators for angular momentum are all well expressed in the bosonic realization with the aid of appropriate entangled states, i.e. we establish a new formalism for the quantum mechanics of a particle on a circle.

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COOPER-PAIR-NUMBER–PHASE SQUEEZING FOR THE BOSONIC HAMILTONIAN MODEL OF JOSEPHSON JUNCTION

Modern Physics Letters B ◽

10.1142/s021798490601127x ◽

2006 ◽

Vol 20 (17) ◽

pp. 1041-1047 ◽

Cited By ~ 5

Author(s):

HONG-YI FAN ◽

JI-SUO WANG ◽

YUE FAN

Keyword(s):

Josephson Junction ◽

Cooper Pair ◽

Entangled State ◽

Entangled State Representation ◽

State Representation ◽

Extra Energy ◽

Bosonic Operator ◽

Hamiltonian Model ◽

Pair Number ◽

Two Sides

Based on Feynman's explanation about the Cooper pair that "a bound pairs act as a Bose particle" and the bosonic operator Hamiltonian of Josephson junction (H.-Y. Fan, Int. J. Mod. Phys. B17 (2003) 2599) as well as the entangled state representation, we establish a possible number–phase squeezing mechanism for the Cooper-pair and the phase difference between the two sides of the junction. We find that when an extra energy (e.g. microwave radiation) is provided to the junction, then this squeezing mechanism can happen.

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APPLICATION OF ENTANGLED STATE IN QUANTIZING SUPERCONDUCTING CAPACITOR MODEL IN THE PRESENCE OF A VOLTAGE BIAS AND A CURRENT BIAS

International Journal of Modern Physics B ◽

10.1142/s0217979204023878 ◽

2004 ◽

Vol 18 (02) ◽

pp. 233-240 ◽

Cited By ~ 11

Author(s):

HONG-YI FAN

Keyword(s):

Operator Theory ◽

Hamiltonian Operator ◽

Entangled State ◽

Entangled State Representation ◽

Phase Operator ◽

State Representation ◽

Voltage Bias ◽

A Current

Based on the entangled state representation and the appropriate bosonic phase operator we develop the superconducting capacitor model in the presence of a voltage bias and a current bias. In so doing, the full Hamiltonian operator theory for a superconducting barrier is established.

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