The double-well potential in quantum mechanics: a simple, numerically exact formulation

被引:64
作者
Jelic, V. [1 ]
Marsiglio, F. [1 ]
机构
[1] Univ Alberta, Dept Phys, Edmonton, AB T6G 2E1, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
FRACTIONAL ELECTRONS; LIQUID-HELIUM; REALITY;
D O I
10.1088/0143-0807/33/6/1651
中图分类号
G40 [教育学];
学科分类号
040101 ; 120403 ;
摘要
The double-well potential is arguably one of the most important potentials in quantum mechanics, because the solution contains the notion of a state as a linear superposition of 'classical' states, a concept which has become very important in quantum information theory. It is therefore desirable to have solutions to simple double-well potentials that are accessible to the undergraduate student. We describe a method for obtaining the numerically exact eigenenergies and eigenstates for such a model, along with the energies obtained through the Wentzel-Kramers-Brillouin (WKB) approximation. The exact solution is accessible with elementary mathematics, though numerical solutions are required. We also find that the WKB approximation is remarkably accurate, not just for the ground state, but also for the excited states.
引用
收藏
页码:1651 / 1666
页数:16
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