A wavefunction crossing a barrier it has not the energy for

At its defaults it draws a wavefunction crossing a barrier it has not the energy for. An electron of 2 electronvolts meeting a 3 electronvolt barrier 0.3 nanometres wide, with the four matching conditions solved rather than sketched. Left of the barrier the incident and reflected waves add to a standing pattern; inside it the amplitude decays exponentially; to the right a travelling wave continues with amplitude 0.3912 of the incident one, so 15.3 per cent of the electrons get through. Classically none of them do.

barrier-tunnel is one function in lib/figures/atomic.js — what happens once one is bound by the other. Everything below came out of it during this build, at parameters taken from the essays rather than invented for this page. A figure here is the figure a reader meets in an essay, and if the generator changes, this page changes with it.

An electron of 2 electronvolts meeting a 3 electronvolt barrier 0.3 nanometres wide, with the four matching conditions solved rather than sketched. Left of the barrier the incident and reflected waves add to a standing pattern; inside it the amplitude decays exponentially; to the right a travelling wave continues with amplitude 0.3912 of the incident one, so 15.3 per cent of the electrons get through. Classically none of them do.

The half-lives of 7 alpha emitters against the reciprocal square root of the alpha's energy — the Geiger–Nuttall coordinates — with the measured values as points and a one-line tunnelling model as the open ones. The energies span a factor of 2.2 and the half-lives span 24 decades, which is what an exponent does. The model has no fitted parameter in it and reproduces every lifetime to within 0.5 decades — bad arithmetic by any ordinary standard, and a hundred-thousandth of the range it is predicting.

The potential an alpha particle sees on its way out of a nucleus of charge 84: a deep well inside the nuclear radius of 9.1 fm, and the Coulomb repulsion of the daughter outside it, rising to 26.6 MeV at the surface. The particle has 5 MeV, so the shaded region between 9.1 fm and the turning point at 48 fm is forbidden to it — a barrier 5.3 times its energy and 39 fm wide. The exponent of the tunnelling probability, integrated across it, is 69.3, which makes the escape probability per attempt about 10^-30.

An electron of 2 electronvolts meeting a 3 electronvolt barrier 0.3 nanometres wide, with the four matching conditions solved rather than sketched. Left of the barrier the incident and reflected waves add to a standing pattern; inside it the amplitude decays exponentially; to the right a travelling wave continues with amplitude 0.3912 of the incident one, so 15.3 per cent of the electrons get through. Classically none of them do.

The probability that an electron of 2 electronvolts crosses a 3 electronvolt barrier, against how wide the barrier is, on a logarithmic scale. It falls from 7.56e-1 at 0.1 nanometres to 1.63e-5 at 1.2 nanometres. The fall is very nearly a straight line on this axis, which means the transmission is exponential in the width: every extra ångström divides it by about 2.8.

The potential an alpha particle sees on its way out of a nucleus of charge 84: a deep well inside the nuclear radius of 9.1 fm, and the Coulomb repulsion of the daughter outside it, rising to 26.6 MeV at the surface. The particle has 8 MeV, so the shaded region between 9.1 fm and the turning point at 30 fm is forbidden to it — a barrier 3.3 times its energy and 21 fm wide. The exponent of the tunnelling probability, integrated across it, is 39.8, which makes the escape probability per attempt about 10^-17.

physicscheck asserts something about barrier-tunnel that could fail — it draws it and measures the result against a value reached some other way.

Across the library: 100 interrogated, 2 exercised only, 1 untouched, of 103. Read out of the gate's source by the gate's own two patterns — and the gate's last claim fails the build if that read disagrees with what it was handed while running.