# Radioactive Decay in the Causal Interpretation of Quantum Theory

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According to classical physics, a particle can never overcome a potential greater than its kinetic energy; this is not the case in quantum theory. For unstable isotopes there is a finite probability for a quantum particle (an particle) to tunnel through the potential barrier in a nucleus. Such isotopes are called radioactive isotopes. The behavior of such isotopes can be described by a square wave packet that is a solution of the Schrödinger equation with the potential term . The time evolution leads to a wave packet that bounces back and forth. Each time it strikes the potential barrier a part of the packet tunnels through and there is a chance for some transmission. In orthodox quantum theory it is impossible to predict the decay of a single isotope. A statistical conclusion can be made only for an ensemble of isotopes (e.g., half-life period).

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Contributed by: Klaus von Bloh (December 2008)

Based on a program by: Enrique Zeleny and Paul Nylander

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The guidance equation for the particle velocity is , which is calculated from the gradient of the phase from the total wavefunction in the eikonal form . The quantum potential is given by . The effective potential is the sum of quantum potential and nuclear potential that leads to the time-dependent quantum force: . The numerical methods to calculate the velocity and the quantum potential from a discrete function are, in general, not very stable, but the applied interpolation functions lead to an accurate approximation of the physical event; due to the numerical errors produced by the limited mesh of 120 mesh points, the velocity term must be adjusted (here using 41/100 instead of 0.5).

References

C. Dewdney and B. J. Hiley, "A Quantum Potential Description of One-Dimensional Time-Dependent Scattering from Square Barriers and Square Wells," *Found. Phys.* 12(1), 1982 pp. 27–48.

J. Caulfield, "What Determines Alpha Decay?," Portsmouth Polytechnic (England), student research project, unpublished, 1991.

A. Goldberg, H. Schey, and J. L. Schwartz, "Computer-Generated Motion Pictures of One-Dimensional Quantum Mechanical Transmission and Reflection Phenomena," *Am. J.* *Phys.*, 35(3), 1967 pp. 177–186.

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