Truncated Gamow functions, ?-decay and the exponential law

Erik Skibsted

A. Bohm, M. Loewe, P. Patuleanu +1 more

Detlef Dürr, Robert Grummt, Martin Kolb

Gamow's explanation of the exponential decay law uses complex "eigenvalues" and exponentially growing "eigenfunctions". This raises the question, how Gamow's description fits into the quantum mechanical description of nature, which is based on real eigenvalues and square integrable wave functions. Observing that the time evolution of any wave function is given by its expansion in generalized eigenfunctions, we shall answer this question in the most straightforward manner, which at the same time is accessible to graduate students and specialists. Moreover the presentation can well be used in physics lectures to students.

R. M. Cavalcanti, C. A. A. de Carvalho

We examine Gamow's method for calculating the decay rate of a wave function initially located within a potential well. Using elementary techniques, we examine a very simple, exactly solvable model, in order to show why it is so reliable for calculating decay rates, in spite of its conceptual problems. We also discuss the regime of validity of the exponential decay law.

Manuel Gadella