EXACT QUANTIZATION CONDITIONS

被引:48
作者
ROSENZWEIG, C
KREIGER, JB
机构
[1] Physics Department, Polytechnic Institute of Brooklyn, Brooklyn, NY
[2] Physics Department, Harvard University, Cambridge, MA
关键词
D O I
10.1063/1.1664651
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
The method of Froman and Froman for proving exact quantization conditions is reviewed. This formalism, unlike the usual WKB approximation to which it bears a close resemblance, requires consideration of the behavior of the potential everywhere it is defined. This approach leads to proofs that certain quantization conditions are exact without having to compare the results to solutions of the Schrödinger equation obtained by other means. Using the formalism, we prove the correctness of all previously known exact quantization rules for the one-dimensional and radial cases. Furthermore, it is shown that exact quantization rules can be proved for two other potentials. For one of these, no analytic solutions to the Schrödinger equation are known. For the latter case, the proof is checked by numerical integration of the Schrödinger equation for a special case.
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页码:849 / +
页数:1
相关论文
共 9 条
[1]  
ARGYRES PN, 1965, PHYSICS, V2, P131
[3]   BOUND ELECTRON PAIRS IN A DEGENERATE FERMI GAS [J].
COOPER, LN .
PHYSICAL REVIEW, 1956, 104 (04) :1189-1190
[4]   The Wentzel-Brillouin-Kramers method of solving the wave equation [J].
Dunham, JL .
PHYSICAL REVIEW, 1932, 41 (06) :713-720
[5]  
Froman N., 1965, JWKB APPROXIMATION C
[6]   APPLICATION OF A HIGHER-ORDER WKB APPROXIMATION TO RADIAL PROBLEMS [J].
KRIEGER, JB ;
ROSENZWEIG, C .
PHYSICAL REVIEW, 1967, 164 (01) :171-+
[7]   USE OF WKB METHOD FOR OBTAINING ENERGY EIGENVALUES [J].
KRIEGER, JB ;
LEWIS, ML ;
ROSENZWEIG, C .
JOURNAL OF CHEMICAL PHYSICS, 1967, 47 (08) :2942-+
[8]   ASYMPTOTIC PROPERTIES OF PERTURBATION THEORY [J].
KRIEGER, JB .
JOURNAL OF MATHEMATICAL PHYSICS, 1968, 9 (03) :432-&
[9]   On the connection formulas and the solutions of the wave equation [J].
Langer, RE .
PHYSICAL REVIEW, 1937, 51 (08) :0669-0676