Noncentral Forces in Three Dimensions: A Brief Survey
As far as the study of NC systems in 3D (whether at the classical or quantum level) is concerned, not many efforts have been made in the literature except for the possibilities of extending the methods and techniques developed already for 1D or 2D systems. Even in this case the central force problems investigated in 3D do not lie within the purview of this chapter and we avoid their discussion. Therefore, we shall make a few remarks (more or less in a passing manner) on the works carried out on the NC potentials in 3D, discussing both classical and quantum aspects. Although it appears trivial to extend the methods and techniques available already for the 2D systems to the case of 3D systems nevertheless it is necessary to highlight the underlying difficulties in this process. In fact, this is also essential from the point of view of applications of these methods to physical problems in 3D which are perhaps more realistic and occur more frequently than those in 2D. In the next Section, we discuss the classical mechanical aspect of some 3D systems and in Sect. 6.2 the quantum aspect will only be touched upon as sufficient literature is not available on this subject. Some concluding remarks are made in Sect. 6.3.
KeywordsEnergy Shell Quantum Aspect Quartic Oscillator Continue Fraction Method Noncentral Potential
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