Number-Phase Quantization and Deriving Energy-Level Gap of Two LC Circuits with Mutual-Inductance
MENG Xiang-Guo1, WANG Ji-Suo1, ZHAI Yun2, FAN Hong-Yi 3,4
1Department of Physics, Liaocheng University, Shandong 2520592School of Computer Science, Liaocheng University, Shandong 2520593Department of Physics, Shanghai Jiao Tong University, Shanghai 2000304Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026
Number-Phase Quantization and Deriving Energy-Level Gap of Two LC Circuits with Mutual-Inductance
1Department of Physics, Liaocheng University, Shandong 2520592School of Computer Science, Liaocheng University, Shandong 2520593Department of Physics, Shanghai Jiao Tong University, Shanghai 2000304Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026
摘要For two LC circuits with mutual-inductance, we introduce a new quantization scheme in the context of number-phase quantization through the standard Lagrangian formalism. The commutative relation between the charge operator and the magnetic flux operator is derived. Then we use the Heisenberg equation of motion to obtain the current and voltage equation across the inductance and capacity. The results clearly show how the current and voltage in a single LC circuit are affected by the circuit parameters and inductance coupling coefficient. In addition, adopting invariant eigen-operator method the energy-level gap of the dynamic Hamiltonian which describes two LC circuits with mutual-inductance is obtained.
Abstract：For two LC circuits with mutual-inductance, we introduce a new quantization scheme in the context of number-phase quantization through the standard Lagrangian formalism. The commutative relation between the charge operator and the magnetic flux operator is derived. Then we use the Heisenberg equation of motion to obtain the current and voltage equation across the inductance and capacity. The results clearly show how the current and voltage in a single LC circuit are affected by the circuit parameters and inductance coupling coefficient. In addition, adopting invariant eigen-operator method the energy-level gap of the dynamic Hamiltonian which describes two LC circuits with mutual-inductance is obtained.
MENG Xiang-Guo;WANG Ji-Suo;ZHAI Yun;FAN Hong-Yi;. Number-Phase Quantization and Deriving Energy-Level Gap of Two LC Circuits with Mutual-Inductance[J]. 中国物理快报, 2008, 25(4): 1205-1208.
MENG Xiang-Guo, WANG Ji-Suo, ZHAI Yun, FAN Hong-Yi,. Number-Phase Quantization and Deriving Energy-Level Gap of Two LC Circuits with Mutual-Inductance. Chin. Phys. Lett., 2008, 25(4): 1205-1208.
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