We consider a time independent one dimensional finite range and repulsive constant potential barrier between two impenetrable walls. For a nonrelativistic massive particle projected towards the potential with energies...We consider a time independent one dimensional finite range and repulsive constant potential barrier between two impenetrable walls. For a nonrelativistic massive particle projected towards the potential with energies less than the barrier and irrespective of the spatial positioning of the potential allowing for quantum tunneling, analytically we solve the corresponding Schrodinger equation. For a set of suitable parameters utilizing Mathematica we display the wave functions along with their associated probabilities for the entire region. We investigate the sensitivity of the probability distributions as a function of the potential range and display a gallery of our analysis. We extend our analysis for bound state particles confined within constant attractive potentials.展开更多
： The effects of a magnetic field on the vibrational frequency, the ground state energy and the ground state binding energy of a weak-coupling polaron in asymmetrical Gaussian confinement potential quantum well （AGC...： The effects of a magnetic field on the vibrational frequency, the ground state energy and the ground state binding energy of a weak-coupling polaron in asymmetrical Gaussian confinement potential quantum well （AGCPQW） are investigated by using linear combination operator and unitary transformation methods. Our cal- culated results show that the vibrational frequency increases with increasing cyclotron frequency of the magnetic field; meanwhile, the absolute value of the ground state energy and the ground state binding energy decrease. The vibrational frequency, the absolute value of the ground state energy and the ground state binding energy are in- creasing functions of the barrier height of the AGCPQW. It is shown that the barrier height of the AGCPQW and the magnetic field are important factors that influence the properties of the magnetopolaron in AGCPQW.展开更多
With the circumstance of the electron strongly coupled to LO-phonon and using the variational method of Pekar type（VMPT）,we study the eigenenergies and the eigenfunctions（EE） of the ground and the first excited st...With the circumstance of the electron strongly coupled to LO-phonon and using the variational method of Pekar type（VMPT）,we study the eigenenergies and the eigenfunctions（EE） of the ground and the first excited states（GFES） in a RbCl crystal asymmetric Gaussian potential quantum well（AGPQW）.It concludes：（i） Twoenergy-level of the AGPQW may be seen as a qubit.（ii） When the electron located in the superposition state of the two-energy-level system,the time evolution and the coordinate changes of the electron probability density oscillated periodically in the AGPQW with every certain period T0=22.475 fs.（iii） Due to the confinement that is a two dimensional x-y plane symmetric structure in the AGPQW and the asymmetrical Gaussian potential（AGP） in the AGPQW growth direction,the electron probability density presents only one peak configuration located in the coordinate of z 〉 0,whereas it is zero in the range of z 〈 0.（iv） The oscillatory period is a decreasing function of the AGPQW height and the polaron radius,（v） The oscillating period is a decreasing one in the confinement potential R 〈 0.24 nm,whereas it is an increasing one in the confinement potential R 〉 0.24 nm and it takes a minimum value in R = 0.24 nm.展开更多
针对量子粒子群算法在处理自变量具有有限定义域的问题时易陷入局部最优解的问题,对算法的量子模型加以改进,提出了基于非对称势的量子粒子群算法(asymmetric potential well based quantum particle swarm optimization,AQPSO)。该算...针对量子粒子群算法在处理自变量具有有限定义域的问题时易陷入局部最优解的问题,对算法的量子模型加以改进,提出了基于非对称势的量子粒子群算法(asymmetric potential well based quantum particle swarm optimization,AQPSO)。该算法认为粒子处于非对称势阱中,势阱的参数由当前的最优位置和自变量的定义域共同决定。而在求解粒子在空间分布的波函数时,又采用了参数消减方法,只需人工指定越限概率,简化算法流程。最后,通过算例验证,该方法的全局搜索能力显著提升,在处理高维、复杂、强干扰性问题时,具有显著优势。展开更多
文摘We consider a time independent one dimensional finite range and repulsive constant potential barrier between two impenetrable walls. For a nonrelativistic massive particle projected towards the potential with energies less than the barrier and irrespective of the spatial positioning of the potential allowing for quantum tunneling, analytically we solve the corresponding Schrodinger equation. For a set of suitable parameters utilizing Mathematica we display the wave functions along with their associated probabilities for the entire region. We investigate the sensitivity of the probability distributions as a function of the potential range and display a gallery of our analysis. We extend our analysis for bound state particles confined within constant attractive potentials.
基金Project supported by the National Natural Science Foundation of China(Nos.11464033,11464034)
文摘： The effects of a magnetic field on the vibrational frequency, the ground state energy and the ground state binding energy of a weak-coupling polaron in asymmetrical Gaussian confinement potential quantum well （AGCPQW） are investigated by using linear combination operator and unitary transformation methods. Our cal- culated results show that the vibrational frequency increases with increasing cyclotron frequency of the magnetic field; meanwhile, the absolute value of the ground state energy and the ground state binding energy decrease. The vibrational frequency, the absolute value of the ground state energy and the ground state binding energy are in- creasing functions of the barrier height of the AGCPQW. It is shown that the barrier height of the AGCPQW and the magnetic field are important factors that influence the properties of the magnetopolaron in AGCPQW.
基金Project supported by the National Natural Science Foundation of China(No.11464033)the Mongolia University for Nationalities Fund(No.NMDYB1445)
文摘With the circumstance of the electron strongly coupled to LO-phonon and using the variational method of Pekar type（VMPT）,we study the eigenenergies and the eigenfunctions（EE） of the ground and the first excited states（GFES） in a RbCl crystal asymmetric Gaussian potential quantum well（AGPQW）.It concludes：（i） Twoenergy-level of the AGPQW may be seen as a qubit.（ii） When the electron located in the superposition state of the two-energy-level system,the time evolution and the coordinate changes of the electron probability density oscillated periodically in the AGPQW with every certain period T0=22.475 fs.（iii） Due to the confinement that is a two dimensional x-y plane symmetric structure in the AGPQW and the asymmetrical Gaussian potential（AGP） in the AGPQW growth direction,the electron probability density presents only one peak configuration located in the coordinate of z 〉 0,whereas it is zero in the range of z 〈 0.（iv） The oscillatory period is a decreasing function of the AGPQW height and the polaron radius,（v） The oscillating period is a decreasing one in the confinement potential R 〈 0.24 nm,whereas it is an increasing one in the confinement potential R 〉 0.24 nm and it takes a minimum value in R = 0.24 nm.
文摘针对量子粒子群算法在处理自变量具有有限定义域的问题时易陷入局部最优解的问题,对算法的量子模型加以改进,提出了基于非对称势的量子粒子群算法(asymmetric potential well based quantum particle swarm optimization,AQPSO)。该算法认为粒子处于非对称势阱中,势阱的参数由当前的最优位置和自变量的定义域共同决定。而在求解粒子在空间分布的波函数时,又采用了参数消减方法,只需人工指定越限概率,简化算法流程。最后,通过算例验证,该方法的全局搜索能力显著提升,在处理高维、复杂、强干扰性问题时,具有显著优势。
