一维线性谐振子相干态随时间的演化

Evolution of the coherent states of one-dimensional linear harmonic oscillator

线性谐振子在量子力学中是非常重要的一个理论模型.通过引入湮灭算符和产生算符,把线性谐振子的哈密顿量转化成粒子数表象下的形式,避免了复杂的运算,容易导出一维线性谐振子的能量本征值和本征函数.把相干态展开为谐振子本征态的线性叠加,最后得到一维线性谐振子相干态在坐标表象下随时间的演化关系.发现其相干态是以不同频率随时间振动的一系列波包.

The linear harmonic oscillator is a very important theoretical model in quantum mechanics.By introducing the annihilation operator and the generation operator,the Hamiltonian of the linear harmonic oscillator is transformed into the form under the representation of the particle number,which avoids complex operations and tends to derive the energy eigenvalue and eigenfunction of the one-dimensional linear harmonic oscillator.The coherent state is expanded as a linear superposition of the eigenstates of the harmonic oscillators,and finally the evolution relationship of the coherent states over time under the coordinate representation can be obtained.It is found that the coherent state is a series of wave packets vibrating with time at different frequencies.