Double-well potential

The so-called double-well potential is one of a number of quartic potentials of considerable interest in quantum mechanics, in quantum field theory and elsewhere for the exploration of various physical phenomena or mathematical properties since it permits in many cases explicit calculation without over-simplification. The so-called double-well potential is one of a number of quartic potentials of considerable interest in quantum mechanics, in quantum field theory and elsewhere for the exploration of various physical phenomena or mathematical properties since it permits in many cases explicit calculation without over-simplification. Thus the 'symmetric double-well potential' served for many years as a model to illustrate the concept of instanton as a pseudo-classical configuration in a Euclideanised field theory. In the simpler quantum mechanical context this potential served as a model for the evaluation of Feynman path integrals. or the solution of the Schrödinger equation by various methods for the purpose of obtaining explicitly the energy eigenvalues. The 'inverted symmetric double-well potential', on the other hand, served as a nontrivial potential in the Schrödinger equation for the calculation of decay rates and the exploration of the large order behavior of asymptotic expansions.