Quantized Damping Behavior Of The One-dimensional Oscillator And Its Application

The one-dimensional oscillator model is widely quoted in the explanation of the interaction between light and matter due to its clearly physical image and easily mathematical treatment.However,this model does not show any relationship to the energy level structure of the related atom(or molecules).So it is not regarded to be an available model.By introducing the new concept of quantized capacitance and resistance into the classical oscillator,we proposed the one-dimensional oscillator model with quantized impedance and introduced the eigenfrequency of electron transition of hydrogen into the classical one-dimensional oscillator model successfully.Based on this model,we put forward to the concept of quantized collision cross section and the corresponding mean collision frequency in the electron transition process.We simulated hydrogen atom emission spectrum,and investigated the hydrogen and hydrogen-like atom spectrum in detail using the oscillator with the quantized impedance.The main achievements of our effort are as following:1.In the quantization of one dimensional oscillator damping model we presented the concept of quantized collision cross section in the electron transition process.Using theoretical calculation and other methods,we fit with the experimental spectrum of hydrogen atom.In the case of the hydrogen atom,based on the one-dimensional oscillator with the quantized impedance,we proposed the concept of quantized collision cross section in the electron transition process and obtained the results that the damping coefficient of the classical oscillator is just the mean collision frequency of the transition electron process,and is proportional to the quantized collision cross section.According to Boltzmann distribution theory,we worked out theoretically that the average collision frequency is mainly caused by collision between the ground state of atoms and transition electron.Based on the general theory of electric polarization of medium,we numerically fit hydrogen atom emission spectrum,the results are well in accordance with the experimental results.2.Broaden effects of temperature on the spectrum of hydrogen and sodium atoms.Based on our model(the one-dimensional oscillator with the quantized impedance model),after theoretical analysis,we obtain that the FWHM of spectrum of hydrogen and sodium atoms is proportional to temperature of the 1/2 party.The theoretical curve showed that the FWHMs of hydrogen and sodium atomic spectrum broadening along with the temperature increase.3.Dielectric constant of hydrogen-like atom medium-aluminum metal.Take aluminum atom for instance,we investigated the numerical characteristic curve of the dielectric constant changed with frequency,and compared to that of Drude model.Results showed that our model can be transited to Drude model as the light frequency deviating from the linear absorption area of this metal.The results above show that: it is likely to make the famous model used to estimate the refractive index of hydrogen and the like atoms and also physical problems such as singleand multi-photon absorption by introducing the concept of quantized reactance and quantized collision cross section into the classical one-dimensional oscillator model...