Abstract
A quantized impedance is proposed to theoretically establish the relationship between the atomic eigenfrequency and the intrinsic frequency of the one-dimensional oscillator in this paper. The classical oscillator is modified by the idea that the electron transition is treated as a charge-discharge process of a suggested capacitor with the capacitive energy equal to the energy level difference of the jumping electron. The quantized capacitance of the impedance interacting with the jumping electron can lead the resonant frequency of the oscillator to the same as the atomic eigenfrequency. The quantized resistance reflects that the damping coefficient of the oscillator is the mean collision frequency of the transition electron. In addition, the first and third order electric susceptibilities based on the oscillator are accordingly quantized. Our simulation of the hydrogen atom emission spectrum based on the proposed method agrees well with the experimental one. Our results exhibits that the one-dimensional oscillator with the quantized impedance may become useful in the estimations of the refractive index and one- or multi-photon absorption coefficients of some nonmagnetic media composed of hydrogen-like atoms.
Highlights
The absorptive spectrum is of vital importance because it can reveal the optical characteristics of many materials
The quantized capacitance of the impedance interacting with the jumping electron can lead the resonant frequency of the oscillator to the same as the atomic eigenfrequency
The quantized resistance reflects that the damping coefficient of the oscillator is the mean collision frequency of the transition electron
Summary
The absorptive spectrum is of vital importance because it can reveal the optical characteristics of many materials. The third one is often in relation to two-photon absorption (TPA), the third-harmonic generation, Optical Kerr effect, and other nonlinear optical phenomena It is well-known that the one-dimensional oscillator can exhibit a clear and understandable physical image in interpreting the interaction of light-matter without the difficulty of the mathematic treatment. The damping coefficient (2Γ) of the electronic movement cannot be estimated due to the lack of physical expression in detail This known model is not regarded as a practical method in explaining the absorptive behaviors of media.[11] It may be an interesting topic to find out a way to establish the relationship between the oscillator and the atom energy level structure. We use the modified oscillator with the quantized impedance to investigate the hydrogen atom spectrum in detail
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