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词汇 Harmonic potential
分类 英语词汇 英语翻译词典
释义

Harmonic potential

中文百科

量子谐振子 Quantum harmonic oscillator

（重定向自Harmonic potential）
能量最低的六个束缚本征态的波函数表征（n = 0到7）。横轴表示位置x。此图未经归一化。
束缚本征态之机率密度|ψn(x)|²，从最底部的基态（n = 0）开始，往上能量逐渐增加。横轴表示位置x，而较亮的色彩代表较高的机率密度。

在量子力学里，量子谐振子（英语：quantum harmonic oscillator）是古典谐振子的延伸。其为量子力学中数个重要的模型系统中的一者，因为一任意势在稳定平衡点附近可以用谐振子势来近似。此外，其也是少数几个存在简单解析解的量子系统。量子谐振子可用来近似描述分子振动。

英语百科

Quantum harmonic oscillator 量子谐振子

（重定向自Harmonic potential）
Some trajectories of a harmonic oscillator according to Newton's laws of classical mechanics (A–B), and according to the Schrödinger equation of quantum mechanics (C–H). In A–B, the particle (represented as a ball attached to a spring) oscillates back and forth. In C–H, some solutions to the Schrödinger Equation are shown, where the horizontal axis is position, and the vertical axis is the real part (blue) or imaginary part (red) of the wavefunction. C, D, E, F, but not G, H, are energy eigenstates. H is a coherent state—a quantum state that approximates the classical trajectory.
Wavefunction representations for the first eight bound eigenstates, n = 0 to 7. The horizontal axis shows the position x. Note: The graphs are not normalized, and the signs of some of the functions differ from those given in the text.
Corresponding probability densities.
Probability densities |ψn(x)|2 for the bound eigenstates, beginning with the ground state (n = 0) at the bottom and increasing in energy toward the top. The horizontal axis shows the position x, and brighter colors represent higher probability densities.

The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics. Furthermore, it is one of the few quantum-mechanical systems for which an exact, analytical solution is known.
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