Atom In A Box

READ ME for Atom in a Box v1.0 by Dean Dauger What is Atom in a Box? Atom in a Box is an application that aids in visualizing the Hydrogenic atomic orbitals, a prime and otherwise unwieldy example of quantum mechanics. Unlike other tools in this category, this program raytraces through a three-dimensional cloud density that represents the wavefunction's probability density and presents its results in real-time (up to 48 frames per second on the latest hardware). The user interface is very interactive and provides a wide degree of flexibility. It contains all 140 eigenstates up to the n=7 energy level and the allowed spectral transitions between those eigenstates. It also allows a state formed by a superposition of up to eight of those eigenstates allowing for over 3 trillion possible states. The program can display a wavefunction as a picture of a cloud, use color as phase, plot in red-cyan left/right for 3D glasses, and slice the wavefunction. How do I use Atom in a Box? The bottom line is: PLAY WITH IT! Go ahead and try anything your heart desires. Most Macintosh users skip manuals anyway, and the program displays help text and help balloons for almost all items in the window. This Read Me is meant for those who want more details about the program but is not required reading. What are Orbitals? "Orbital" is the name given to the state of an electron bound to an atomic nucleus, analogous to the orbit a planet occupies around a star. The primary differences are that the orbital is described by Quantum Mechanics and the interaction is electromagnetism. Special states, called eigenstates, have been found that, when properly summed together, can describe any allowed state of the electron bound to the nucleus. By definition, they cannot -1- be written in terms of one another (i.e., they are said to be "orthogonal"). These eigenstates have their own unique labels. The first refers to the energy of the eigenstate, labeled by n. n can be any integer starting at one, the lowest energy level, then two, three, and so on for higher energies. Within an energy level, there are certain allowed distinct states of angular momentum which are identified by two integers, l and m. l, which identifies how much angular momentum the eigenstate has, ranges from zero to n-1. m, which identifies how much of that angular momentum is in the +z-direction, ranges from negative l to positive l. These three integers together uniquely identify every possible eigenstate, and are often written together in a Dirac ket: |n,l,m>. This code contains parameters for all the eigenstates up to n=7, which is the energy level for the highest energy electrons in the Uranium atom. That makes a total of 140 orthogonal eigenstates. For each eigenstate, the code computes its wavefunction, a complex function of position. The …