N-DIMENSIONAL HARMONIC-OSCILLATOR YIELDS MONOTONIC SERIES FOR THE MATHEMATICAL CONSTANT-PI

被引：6
|
作者：
LYNCH, R [1 ]
MAVROMATIS, HA [1 ]
机构：
[1] KING FAHD UNIV PETR & MINERALS,DEPT PHYS,DHAHRAN 31261,SAUDI ARABIA
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1990年 / 30卷 / 02期
关键词：
N-dimensional harmonic oscillator; Series for π;
D O I：
10.1016/0377-0427(90)90021-Q
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Recently, Mavromatis (1990) has shown that the usual quantum mechanical ideas of matrix elements, expansion in complete sets, and the like, coupled to the three-dimensional harmonic oscillator problem, lead to an infinite set of series expansions for the mathematical constant π. In this paper his results are extended by considering a harmonic oscillator in a general space of N dimensions. It is found that in each odd dimension one obtains series for π, while in each even dimension, series for 1/π. © 1990.
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页码：127 / 137
页数：11
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