Notes on the two-centre problem in wave mechanics. I. The hyperbolic nodes of the wave equation
- 1 January 1939
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 35 (1) , 44-55
- https://doi.org/10.1017/s0305004100020727
Abstract
Approximate expressions are obtained, when the distance R between the nuclei is very large, for that portion of the wave function in the two-centre problem which depends on the hyperbolic coordinate μ. From these expressions the number and the approximate position of the nodes in μ can be deduced and hence the rules can be found by which that state of the combined atom at R = 0 can be determined which corresponds to a given state of the atom when the nuclei are completely separated. These rules are also applicable to the cases where the two atoms which can be formed when the nuclei are completely separated have the same energy. The converse problem of finding what state of the completely separated atom corresponds to a given state of the combined atom at R = 0 can also be solved by the use of the rules.Keywords
This publication has 3 references indexed in Scilit:
- On the energies associated with the two-centre problemMathematical Proceedings of the Cambridge Philosophical Society, 1938
- The Two Centre Problem in Wave MechanicsMathematical Proceedings of the Cambridge Philosophical Society, 1935
- XXI. The addition theorem of the Bessel functions of zero and unit ordersJournal of Computers in Education, 1918