OSP Spins is an interactive computer
program that simulates Stern-Gerlach-type measurements on spin-1/2 and spin-1
particles (a virtual Stern-Gerlach experiment). The original program,
Spins, was written for the Macintosh by Daniel Schroeder and Thomas Moore [Am.
J. Phys. 61, 798 (1993)], and was then ported to Java and called
SPINS by David
McIntyre of Oregon State University. Both of these versions were open
source. We have made extensive modifications to the Java version of
the SPINS program. With the original version, one had to manually set up
scenarios within the applet; these scenarios were then lost when the applet was
closed, thereby limiting the effectiveness of the program. Our
improvements, which appear as the OSP Spins program, include the ability to
script the program using an extensible markup language (xml) data file to enable
different scenarios to be saved and then loaded quickly and easily. This
allows instructors to construct and distribute more interesting virtual
experiments and allows students to spend more time on the physics. In
addition, the user interface can be customized within the xml data file to
reduce the number of options available. This allows teachers to write
curricular material that forces students to interact with the simulation in a
specific way.
The OSP Spins program can be run as a stand alone application, a
browser-based applet, and a Java Web Start application. Because each of
these distribution mechanisms has strengths and weaknesses, we support all three
mechanisms. All versions are available on the Open Source Physics website
and the stand alone version is available on the CD accompanying this report.
A Java application is a program that runs just like any other installed program.
Running an application is the simplest most reliable way to access the Spins
curricular material because the program has complete access to local resources
consistent with the user’s file (security) permissions. Double-click on
the osp_spins.jar file on the accompanying CD to execute the program if the file
system browser associates the “jar” extension with the Java VM.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Spin-1/2 systems are perhaps the simplest, yet interesting, systems to explore the effect of quantum-mechanical measurement on states. There are, in some sense, two different kinds of time evolution in quantum mechanics: predictable time evolution governed by the Schrödinger equation, which in one-dimensional position space is
[−(ħ2/2m)∂2/∂x2 + V(x)] ψ(x,t) = iħ(∂/∂t) ψ(x,t) ,
and the abrupt time evolution (collapse) of wave functions when something is measured. Feynman once stated that "no one understands quantum mechanics," by this he most certainly meant to the collapse of the wave function due to measurement. To complicate matters, multiple measurements in quantum mechanics need not yield the same results due to the uncertainty principle (such as the measurement of x then p then x again).
For a spin-1/2 system, the 1/2 refers to the quantum number s. Spin is spin angular momentum and is related to the intrinsic magnetic moment of a particle. Unlike orbital angular momentum (l = 0, 1, 2,...), spin angular momentum can take on integer and half-integer values (s = 0, 1/2, 1, 3/2, 2,...). Half-integer particles are called fermions (obeying Fermi-Dirac statistics) and integer spin particles are called bosons (obeying Bose-Einstein statistics).