Spectral Behaviors Of One-dimensional Oscillator With Quantized Impedance

The theoretical development of the interaction between light and matter has experienced from the classical theory represented by Lorentz one-dimensional oscillator to Bohr-Sommerfeld’s semi-classical semi-quantum theory and to the numerical simulation theory which is based on the quantum perturbation theory of and first principle.The physical image of the electron motion in the atom corresponding to the Lorentz oscillator is clear,and the mathematical solution is simple and is relatively easy for acceptance.However,since the natural frequency of the vibrator is not uniform with the eigenfrequency of the atomic transition,the damping coefficient of the vibrator is not related to the transition process of the electron,thus the Lorentz oscillator model cannot be used to interpret the spectral characteristics of actual atom.The one-dimensional oscillator mode with quantum impedance damping（referred to“quantum impedance”）was proposed in November 2015.By introducing a quantized reactance damping model associated with the electronic transition process,and using energy conversion and conservation laws,the Lorentz one-dimensional oscillator is quantized.Furthermore,the natural frequency of the vibrator is unified with the eigenfrequency of the transition between the energy levels of the actual atom.We have clarified that the physical meaning of the damping coefficient of the vibrator should be the average collision frequency of other atoms in the electronic transition process.A specific mathematical expression of the damping coefficient consistent with this physical meaning is also given.The theoretical simulation of this model agrees well with the linear absorption spectrum of hydrogen atoms.However,this quantum reactance one-dimensional harmonic oscillator model has not considered the contribution of oscillator strength,nor has it introduced corresponding expression.In addition,the introduction process of this model is mainly for hydrogen atoms,but for hydrogen-like atoms,its applicability needs to be verified by re-characterizing and comparing the results with experimental results.Based on the physical meaning of the oscillator intensity,this paper studies the effect of energy degeneracy on the spectrum in the one-dimensional harmonic oscillator model of the quantified reactance.By means of the concept of quantum defect,it is re-expressed for the model to be used to describe the hydrogen-like atom.And we compared it with the quantum defect of several quantum states of the typical hydrogen-like lithium atom.The linear absorption spectrum of the biological oxidation molecule riboflavin（RBF）,which affects the body,was further studied by the one-dimensional harmonic oscillator model suitable for hydrogen-like atoms.The main results of the paper are as follows.1.The vibrator intensity is introduced into the one-dimensional harmonic oscillator model of the quantized reactance.The influence of the energy degeneracy of Bohr-Sommerfeld theory on the spectral characteristics of the model is studied in detail.Combined with the selection rules of the absorption transition,the hydrogen atom spectrum is numerically simulated.The results show that the energy degeneracy based on Bohr-Sommerfeld theory as the quantum-based reactance one-dimensional harmonic oscillator model of the oscillator strength improves the fitting of the numerical simulation of the hydrogen atom spectrum with the experimental results,and the agreement is better.2.It is assumed that the orbit of a hydrogen-like atom satisfy the Bohr-Sommerfeld quantization condition,and the outermost electron in the direction of the long axis of the ellipse and the motion relative to the nucleus can be regarded as a one-dimensional non-harmonic oscillator of the quantized reactance.The natural frequency and damping coefficient of the transition of the vibrator are re-expressed by means of the concept of quantum defect.On this basis,the calculated quantum defect of the lithium atom at 610.354nm and 670.776 nm is consistent with reported results.The theoretical values of quantum defect and the results of the references are as follows:Theoretical calculation:Δ_2,s=0.439,Δ_2,p=0.041/0.044,Δ_3,d=0.002,Literature reference value:Δ_2,s=0.4115,Δ_2,p=0.0407,Δ_3,d=0.00015.3.Considering a certain atom that forms of a molecule and participating in a transition,is a hydrogen-like atom.According to the peak wavelength and full width at half maximum of the atomic（molecular）linear absorption spectrum,and the selection rule of single photon absorption transition,using the quantized one-dimensional harmonic oscillator model a method for determining the quantum numbers before and after the transition of an atom in an atom（molecular）is proposed.The peak wavelengths of the absorption spectra of the riboflavin（RBF）molecules are corresponded to the resonance wavelengths of the one-dimensional resonators,respectively.By adjusting the damping coefficient of the one-dimensional harmonic oscillator of the quantized reactance to achieve the optimal fitting with the experimental spectrum.The giving damping coefficients are consistent with those of the experimental results.Using the relationship between the damping coefficient and transition frequency and the quantum number of the atomic transition given by the one-dimensional harmonic oscillator model of the quantified reactance,we determined the main quantum number and angular quantum numbers before and after the atomic transition of the atom in the riboflavin molecule which participated in the transition.The optical linear properties such as dispersion and absorption of riboflavin in water are given.The above results show that after considering the quantum defect effect of the atom,the one-dimensional harmonic oscillator model of quantized reactance based on energy degeneracy as one of the main contents of oscillator strength may be used to explain some actual conditions of linear absorption spectrum of an atom or molecule in a certain precision range.