Tunneling and Dynamic Tunneling by an Algebraic Approach

Abstract

Seemingly tunneling is intimately related to a geometrical approach. That however is not always the case as shown by our first example where tunneling connects regions of phase space which are not separated by a potential yet are disjoint in classical mechanics. This example shows that an algebraic approach can handle dynamic tunneling in a bound state system. Recent work has also considerably firmed the geometric interpretation of the algebraic approach. Hence even such traditional problems as barrier penetration can be discussed. To obtain the tunneling rates we discuss the use of non-unitary representations. Towards the extension of the algebraic approach to unbound states in multidimensional systems, the simpler case of an unbound one dimensional motion is discussed and possible generalizations are indicated.