Abstract
The system of a particle moving in a potential field containing two equal minima is treated by the Wentzel-Kramers-Brillouin method of approximation. The energy levels are grouped in pairs and the object of the computation is to find the separation between two levels forming a pair. This is accomplished by connecting the oscillatory and exponential approximate solutions of the wave equation by means of the Kramers connection formulae. If is the separation of a pair and the distance between two pairs where . A particular potential curve is chosen consisting of two equal parabolae connected by a straight line. The expression for may then be evaluated explicitly as a function of the length of the joining line, and the distance between two minima, . These formulae may be applied to determining the form of the ammonia molecule. Substituting the experimental values for and , it is found that and . An exact solution for this particular potential curve may be found by joining Weber's function and to a hyperbolic sine or cosine. This process also leads to expressions for which may be equated to the experimental values yielding and , in good agreement with the earlier determination. Finally is used to compute cm, the distance between the two potential minima, and the following dimensions of the ammonia molecule, H - H = 1.64×, N - H = 1.02× cm.
- Received 8 June 1932
DOI:https://doi.org/10.1103/PhysRev.41.313
©1932 American Physical Society