A convergent iterative solution of the quantum double-well potential

	A convergent iterative solution of the quantum double-well potential
	Friedberg, R; Lee, TD; Zhao WQ(赵维勤); Zhao, WQ; Cimenser, A
刊名	ANNALS OF PHYSICS
	2001
卷号	294 期号:1 页码:#REF!
通讯作者	Friedberg, R (reprint author), Columbia Univ, Dept Phys, 538 W 120th St, New York, NY 10027 USA.
英文摘要	We present a new convergent iterative solution for the two lowest quantum wave functions psi (ev) and psi (od) of the Hamiltonian with a quartic double-weil potential V in one dimension. By starting from a trial function, which is by itself the exact lowest even or odd eigenstate of a different Hamiltonian with a modified potential V + deltaV, we construct the Green's function for the modified potential, The true wave functions, psi (ev) or psi (od), then satisfy a linear inhomogeneous integral equation, in which the inhomogeneous term is the trial function, and the kernel is the product of the Green's function times the sum of deltaV, the potential difference, and the corresponding energy shift. By iterating this equation we obtain successive approximations to the true wave function; furthermore, the approximate energy shift is also adjusted at each iteration so that the approximate wave function is well behaved everywhere. We are able to prove that this iterative procedure converges for both the energy and the wave function at all x. The effectiveness of this iterative process clearly depends on how good the trial function is, or equivalently, how small the potential difference deltaV is. Although each iteration brings a correction smaller than the previous one by a factor proportional to the parameter that characterizes the smallness of deltaV, it is not a power series expansion in the parameter. The exact tunneling information of the modified potential is, of course, contained in the Green's function; by adjusting the kernel of the integral equation via the energy shift at each iteration, we bring enough of this information into the calculation so that each approximate wave function is exponentially tuned. This is the underlying reason why the present method converges, while the usual power series expansion does not. (C) 2001 Elsevier Science.
学科主题	Physics
类目[WOS]	Physics, Multidisciplinary
收录类别	SCI
WOS记录号	WOS:000172677300004
公开日期	2016-05-03
内容类型	期刊论文
源URL	[http://ir.ihep.ac.cn/handle/311005/225893]
专题	高能物理研究所_理论物理室
推荐引用方式 GB/T 7714	Friedberg, R,Lee, TD,Zhao WQ,et al. A convergent iterative solution of the quantum double-well potential[J]. ANNALS OF PHYSICS,2001,294(1):#REF!.
APA	Friedberg, R,Lee, TD,赵维勤,Zhao, WQ,&Cimenser, A.(2001).A convergent iterative solution of the quantum double-well potential.ANNALS OF PHYSICS,294(1),#REF!.
MLA	Friedberg, R,et al."A convergent iterative solution of the quantum double-well potential".ANNALS OF PHYSICS 294.1(2001):#REF!.