利用幺正算符求解耦合谐振子和RLC量子化电路的哈密顿量

Solving Hamiltonian of Coupling Oscillators and RLC Quantization Circuit by Unitary Operator

对于哈密顿量为H=2pm2+γ(qp+pq)+12mω2q2的耦合谐振子和哈密顿量为H=2pL2+2RL(qp+pq)+21Cq2的RLC量子化电路,通过引入幺正算符使其退耦合,给出了该耦合谐振子和RLC量子化电路的能谱信息.计算结果与求解薛定谔方程得到的结果一致,推导过程简洁易懂,该方法能够培养和提升学生运用量子力学解决复杂物理问题的能力.

For coupled oscillators and RLC quantization circuit whose Hamiltonian have been given by ^H=^p^2/2m＋γ（^q^p＋^p^q）＋1/2mω^2^q2 and ^H=^p^2/2L＋R/2L（^q^p＋^p^q）＋1/2C^q^2,respectively,a method of eliminating the coupled item for unitary operators are presented.The energy eigen values of coupling oscillators and RLC quantization circuit obtained by this bandy method are in good agreement with the date calculated by Schrdinger equation.This method could train and improve the ability of students in solving complicated physics problems with quantum mechanics.