奇异电磁场中非对易量子体系研究

发布时间：2018-05-11 09:56

本文选题：偶极子 + 薛定谔方程　；参考：《天津工业大学》2017年硕士论文

【摘要】：本文分别从对易量子力学和非对易量子力学的角度去研究偶极子与电磁场的相互作用,计算偶极子的能量本征值和本征函数。我们将采用具有永久电偶极矩或永久磁矩的中性原子来表征偶极子。在对易量子力学中,我们先回顾了朗道理论,即二维电子气在磁场中的能量量子化问题。基于朗道能级我们先后研究了磁偶极子与电场的相互作用,电偶极子与奇异磁场的相互作用以及电偶极子与电磁场的相互作用。我们发现只有满足特定的三个条件中性原子在电磁场中的能量才会出现类朗道能级的量子化现象。并且在求解薛定谔方程时,我们还发现,在以上给出的三种场-偶模型中,它们的定态薛定谔方程都能转化为合流超几何方程,因此,我们只需根据合流超几何方程的解的固有形式,就可写出在不同场-偶模型下的偶极子的能量本征值和本征函数。在非对易量子力学中,我们对非对易空间和非对易相空间进行了介绍,然后我们利用Bopp变换分别求出了在非对易空间及非对易相空间中电偶极子与电磁场相互作用的哈密顿量,计算了电偶极子的能量本征值和本征函数。最后我们再把该计算结果同对易量子力学下的结论进行比较,我们把θ和θ修正的哈密顿量当作微扰项,计算了电偶极子能级的非对易修正,并分析了非对易性引起的能量差的消除条件。
[Abstract]:In this paper, the interaction between dipole and electromagnetic field is studied from the point of view of commutative quantum mechanics and non-commutative quantum mechanics, and the energy eigenvalue and eigenfunction of dipole are calculated. We will use neutral atoms with permanent electric dipole or permanent magnetic moment to characterize the dipole. In terms of easy quantum mechanics, we first review Landau's theory, that is, the energy quantization of two-dimensional electron gas in magnetic field. Based on the Landau energy level, we have studied the interaction between magnetic dipole and electric field, the interaction between electric dipole and singular magnetic field, and the interaction between electric dipole and electromagnetic field. We find that only when the energy of neutral atom in electromagnetic field satisfies three special conditions can the quantum phenomenon of Landau level appear. In solving the Schrodinger equation, we also find that their stationary Schrodinger equations can be transformed into confluent hypergeometric equations in the three field-couple models given above. We can write the energy eigenvalues and eigenfunctions of dipoles under different field-even models only according to the inherent form of solutions of the confluence hypergeometric equations. In non-commutative quantum mechanics, we introduce non-commutative space and non-commutative phase space, then we use Bopp transform to calculate the Hamiltonian of electric dipole interaction with electromagnetic field in non-commutative space and non-commutative phase space, respectively. The energy eigenvalues and eigenfunctions of electric dipoles are calculated. Finally, we compare the calculated results with the conclusions of the quantum-free mechanics. We take theta and 胃 modified Hamiltonian as perturbation terms and calculate the noncommutative correction of the electric dipole energy levels. The conditions for eliminating the energy difference caused by non-commutativity are analyzed.
【学位授予单位】：天津工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O413.1

【参考文献】