Real-Time Visualization of the Quantum Mechanical Atomic Orbitals The orbital images on this page represent the shape of the atomic orbitals. The clouds you see are the probability distribution of an electron bound to a Hydrogen nucleus. These images were created using Atom in a Box, a scientific and educational program that aids in visualizing the Hydrogenic atomic orbitals, a prime and otherwise unwieldy example of quantum mechanics. Goo building mac os. |
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Games Like Worbital for Mac OS. Game's Complex and realistic Orbital Physics helps players learn about the Hohmann Transfer Orbits (Start from a Lower Orbit and end up in a Higher Orbit) maneuvers and enjoy piloting the ship. According to the gameplay and game story, the game tasks the players to head a Nascent Space Program, Control the. Magnussoft ZETA, earlier yellowTAB ZETA, was an operating system formerly developed by yellowTAB of Germany based on the Be Operating System developed by Be Inc.; because of yellowTAB's insolvency, ZETA was later being developed by an independent team of.
| Mac | iPhone | iPad |
Atom in a Box on the Mac App Store for both Apple Silicon and Intel Macs running macOS 'Big Sur' 11.2 or later See below for additional Mac versions. | Atom in a Box for the iPod Touch and iPhone is part of the debut of the App Store. |
NOTE: First announced at the 1998 Conference on Computational Physics held in Granada, Spain, I am a student winner in Computers In Physics' Ninth Annual Software Contest with Atom in a Box. Krong thips mac os. Full descriptions of the prize winners are in CIP's Nov/Dec 1998 issue. This now makes me the only person to have been a student winner twice in a row in CIP's Software Contest. In addition, Apple has been kind enough to write an article about Atom in a Box in their inaugural issue of Apple University Arts. Do you speak Dutch? Prata svenska? Sprechen Sie Deutsch? Habla español? Parlez-vous Français? Parlate italiano? Also, this program appears in a 12-minute streaming RealVideo clip at the UCLA Department of Design. In addition to the many kind individuals who have registered, I thank all those who registered from institutions such as: Massachusetts Institute of Technology, Pacific Lutheran University, U. C. Davis, Georgia Institute of Technology, Pennsylvania State University, University of Houston, Wesleyan University, University of Missouri - St. Louis, Purdue University, Millikin University, West Virginia University, Karl-Franzens-Universität Graz, Universität Bern, Washington State University, Southwest Missouri State University, Douglas High School, San Joaquin Delta College, Maine Maritime Academy, Kalamazoo College, Southwestern University - Georgetown, Texas, Haverford College, Florida A&M University, Nagoya University, Miami University, Virginia Tech, Yale University, Bob Jones University, Cornell University, Kyoto University, Utah State, Institute for Advanced Study at Princeton, Snow College, Hammond High School, Reed College, University of Washington, Wooster College, Colorado School of Mines, the Wellington School, the University of Southern Mississippi, Harvey Mudd College. Many people have registered from outside the United States: Japan, United Kingdom, Canada, Austria, Switzerland, Belgium, Germany, and Italy. Through word of mouth, I have heard of my program in use at Caltech, U. C. Santa Cruz, Stanford, Harvard, and others. |
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 Mac G3s; even faster 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. The Mac version also allows a state formed by a superposition (see below) of up to eight of those eigenstates allowing for over 3 trillion possible states and 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.
You can see more example images at the bottom of the page.
What is Quantum Mechanics?
One of the great advances in human knowledge of the twentieth century is the birth of the theory of Quantum mechanics. It has led to some of the most common technologies used today, including the little transistors that make up the computers you're using to read this. One of the mysteries it revealed was the structure of the atom. Classical mechanics could not properly explain the existence of the atom. Because there was nothing to stop electrons from spiralling in to the nucleus, it predicted that all atoms would immediately destroy themselves in a spectacular high-energy blast of radiation.
Well, that obviously doesn't happen. Quantum mechanics describes that the electron (and all of the universe for that matter) exists in any of a multitude of states. The particular physical situation determines what and how many states there are. Borrowing from some of the techniques in mathematics, physicists organize these states into a particular set of mathematically convenient states called 'eigenstates'. Eigenstates are good to use because what makes one eigenstate different from another usually has a physical meaning. They also can make an horribly difficult problem managable. These and other phenomena in Quantum mechanics predict that possiblities in physical phenomena have distinct separations (e.g., 'quantum leaps') and that energy transport exists as indivisible packets, called 'quanta'. Hence the name: Quantum Mechanics.
What are Orbitals?
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By applying these techniques to the hydrogen atom, physicists are able to precisely predict all of its properties. The electron eigenstates around the nucleus are called 'orbitals', in a rough correspondence with how the Moon orbits the Earth. We find that these states do not allow the electron to crash into the nucleus, but instead find themselves in any combination of these orbital eigenstates. These orbitals' physical structure describe effects from how atoms bond to form compounds, magnetism, the size of atoms, the structure of crystals, to the structure of matter that we see around us.
Visualizing these states has been a challenge, because the mathematics that describe the eigenfunctions are not simple and the states are a three-dimensional structures. The standard convention has the orbital eigenstates indexed by three interrelated integer indicies, called n, l, and m. Their range and interdependence comes out of the math in deriving the eigenstates. n can range from 1 to infinity. l can range from 0 to n-1. m can range from -l to +l. They also have physical meaning. The energy of the state, which is negative because the electron is bound to the nucleus, depends only on n and increases as n increases. l refers to the amount of angular momentum the electron has due to its 'orbit' around the nucleus. l is not equal to the amount of angular momentum but goes up as angular momentum goes up. m determines how much of the angular momentum is in the z direction. (However, the rest of the angular momentum is not l minus m or anything that simple. That's a long story that I can't fit here. Look in a Quantum textbook (a good one is A Modern Approach to Quantum Mechanics by John S. Townsend), take a course, or talk to a physics professor.)
What's here for me?
I have written a Macintosh application that displays atomic orbitals in real-time. Rather than just a plot of the spherical harmonics, as is shown in many Quantum mechanics textbooks, this program displays the electron orbital as a cloud. The cloud's density is determined by the orbital's probability density for the electron. There are three examples on this web page: The one at the top is the n=3, l=2, m=0 state; the screenshot above has n=7, l=4, m=0; the first example below is n=6, l=4, m=1. (The quality is poor so that they wouldn't take too long to download over the Internet. They'll look even worse if you are not using Millions of colors to view it. The program looks quite a bit better, trust me.) With the program, you can rotate the orbital around in real time. If you have red-cyan 3-D glasses, you can see it in 3-D too. The program has all the orbital eigenstates up to n=7, which is the highest occupied shell for the ground states of the heaviest elements, e.g., Uranium, Plutonium, etc.
You can download the application from the links below and have a look. The program is computation intensive. For individual users, the v1.x Mac application is US $20 shareware. Pricing of the later versions are on the App Store. You can read the details in the about box or the Read Me. Also supplied are example orbital files.
Platform Availability| Mac | iPhone and iPod Touch | iPad | |||||
Depersonalization mac os. Rewritten from the ground up, v2 of Atom in a Box uses SwiftUI 2.0 and multicore to reach new capabilities the previous code could never do.
After Mojave, Apple ended support for the Carbon API this app uses. If you're not sure if it'll run on your macOS, you may download it so you can test. This code base will receive no further updates. In 2006, the Universal Binary version included the following enhancements: QuickTime export of the orbital animation, in addition to PICS. Endian conversions for file and disk access. Adapted source to Xcode. OS X-compliant application and file icons and plst data. Correction of an issue with sound buffers for the orbital sound. New recognition of horizontal and vertical scroll wheels, so now you can use the Mighty Mouse's scroll ball to rotate the orbital. Known issue in the Universal version: On most Macs, OS X 10.4.x places a 60 fps governor on QDFlushPortBuffer, consequently limiting the speed with which AiB can display its animation. One should be aware of that before making speed comparisons. Hint: increase the Samples setting to make the calculations more challenging. For OS 9 and pre-OS X 10.3.9, we also provide a Carbon CFM version of AiB 1.1 (324 kB). v1.0.6 will run on both OS 9 (with CarbonLib) and OS X. The latest pre-Carbon version of Atom in a Box, v1.0.4 is no longer supported. See the READ ME for more details. | Atom in a Box -
See the App Store for pricing and availability for your country. |
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See the Atom in a Box iOS Online FAQ for Version History. Reviewers: Please email your request and your background info (e.g., your web site) to feedback @ daugerresearch.com to obtain a review copy. |
A Short Gallery of Animated Orbitals
This is the quantum state where n=6, l=4, and m=1: | Orbital Animation' src='Orbital.641.small.gif' width=192 align=center> |
This is an equal superposition of the |3,2,1> and |3,1,-1> eigenstates: | +|3,1,-1> Orbital Animation' src='Orbital.321+31-1.gif' width=192 align=center> |
This is an equal superposition of the |3,2,2> and |3,1,-1> eigenstates: | +|3,1,-1> Orbital Animation' src='Orbital.322+31-1.gif' width=192 align=center> |
This is an equal superposition of the |4,3,3> and |4,1,0> eigenstates: | +|4,3,3> Orbital Animation' src='Orbital.410+433.gif' width=192 align=center> |
File system metainformation
Install DP2 on an HFS+ volume and as expected, you get full support for classic Mac OS files and applications with resource forks. Carbon applications also use resource forks, making it clear that the default file system for Mac OS X will end up being HFS+ if only to ensure the promised ability to sell the same Carbon applications to both Mac OS 9.x and Mac OS X users.
But the future of meta-information in Mac OS X is less clear. Resource forks remain for the sake of the transitional API, Carbon. But even Carbon apps are moving away from the traditional Mac OS multi-fork concept and into the realm of NeXT-derived 'application wrappers' (also called 'bundles' in NEXTSTEP and 'packages' in Mac OS 9 and Mac OS X). Put simply, a package is a structured collection of files and directories that is treated specially by the high-level UI. In DP2, packages are identified by a '.app' extension. In Mac OS 9, packages are identified by a particular Finder flag.
Let's look at the Carbonized version of the venerable Mac OS FTP application 'Fetch' that's included with DP2. From DP2's Finder-like interface, it looks like this:
Fetch.app launches and runs as expected with a simple double-click. But from the command line, it looks like what it really is: a directory with a bunch of other files and directories inside it. The contents look like this:
The business end of the package is the 'Executables' directory, which is further subdivided by operating system (Hmmm..). The file 'Fetch' at the tail end of that directory is much like a classic Mac OS application. It has a resource fork filled with pretty much the same stuff as the classic version of Fetch. It has a file type of 'APPL'. It launches the application when you run it, even from the command line.
So why go through the whole charade of wrapping our little application in this structure? The answer lies in the contents of the other files inside the package, and the future direction of meta-information in Mac OS X. Let's look at the other files in the package more closely.
The file 'Info-macosx.plist' is actually an XML property list ('plist') containing a lot of the same meta-information traditionally stored in the classic Mac OS resource fork. Here's a small snippet:
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AdvertisementFrom this we learn a few things. To start, it appears that the XML document type definition ('DTD') is stored locally, allowing for easy changes to the format of this file (unlike changes to the format of, say, Finder meta-information in classic Mac OS. Any changes to that structure require major OS revisions!) But the DTD location is given as a URL, opening the door for it to be located anywhere in the world.
Next, we see the use of the old NeXT term 'bundle' in the key names. The 'CF' prefix refers to Apple's 'Core Foundation' libraries which provide basic resources like string classes, collections, and dictionaries to higher-level Mac OS X APIs like Carbon and Cocoa.
Finally, traditional Mac OS meta-information is easily recognizable in the plist file: type APPL, creator FTCh, version 3.0.3d0, language English, and so on. This file goes on for about 100 lines and includes many more key/value pairs and other deeper structures. It's not clear whether or not Mac OS X is reading the .plist file or the Fetch executable's resource fork. Mac OS 9, at least only needs the Fetch executable itself to run Fetch.app.
Peeking inside the 'PkgInfo' file reveals yet another duplication of meta-information, but this time just the essentials: type and creator. It simply contains the text 'APPLFTch'
The rest of the files are icons: a NeXT-style TIFF and a bunch of Mac OS 8.5/9.0 style 'icns' resources. Again, the icns resources are duplicated within the Fetch executable's resource fork.
Now let's take a look at a Cocoa application package: Chess.app
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Every file in this package is a simple, flat file, including the 'Chess' executable itself (unlike Fetch.app's executable with its resource fork). In place of the Mac OS resource fork, there are various '.nib' files (inside a 'Chess.nib' directory). These files (created by Interface Builder, the NeXT-derived GUI layout tool) contain all the interface data usually stored in Mac OS resource forks. 'classes.nib' is a plain text file in a proprietary (but very simple to understand) format that defines the attributes for each interface object class. The 'obects.nib' file is the binary data for the interface objects themselves. I've heard talk of Apple changing the '.nib' file format to XML, but this change is not present in DP2.
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AdvertisementThe rest of the files in the package: images, icons (in two formats), sounds, the required GNU license file ('COPYING'), some miscellaneous plain text data files, and even the application credits in the form of an RTF file. The XML 'plist' and the simple 'PkgInfo' files are also present.
Packaged Future
The future direction of meta-information in Mac OS applications is clear: packages. (..or 'bundles', or 'application wrappers', depending on who you ask. But 'packages' is the official Apple name as of the release of Mac OS 9.0.) Resource forks will stick around for a while, but their long-term future is uncertain.
And yes, for those not following along, the upshot of all this package business is that Mac OS X applications like the Chess.app will travel across any foreign file system with no loss of meta-information or resources. Tar it, zip it, FTP it, it'll always stay perfectly intact. Hurray for technology NeXT had in the 1980's!
Before I leave the topic of meta-information, there's one small wrinkle in this packages-scheme. Earlier I mentioned that the higher-level Finder-like UI in DP2 recognizes packages by the '.app' extension and shows them as normal applications (see the screenshot of Fetch.app above) instead of showing them as what they really are: directories. I also mentioned that packages in Mac OS 9 are identified by a particular Finder flag. But Finder flags are file system dependent. Copy a file from an HFS or HFS+ volume to a FAT or UFS file system and those Finder flags are gone.
This is part of the motivation for the concept of packages, of course, but without the very thing that packages are meant to eliminate (HFS/HFS+ dependent meta-information), how will packages be identified in Mac OS 9 or the release of Mac OS X? Is that '.app' extension really going to stick around? File extensions have never been a part of the Mac OS user experience, so even if they do stick around in Mac OS X, expect them to be hidden by the higher-level UI. In Mac OS 9, I suspect the Finder flag will stick around. This makes sense since Carbon apps have resource forks in their executables--another feature that requires HFS+ or HFS. So the ability to store Finder flags is essentially guaranteed in Mac OS 9.
File name extensions in Mac OS X are a much fuzzier subject. Every file in classic Mac OS has a type and creator, but only packages in Mac OS X have this meta-information. Will every file in Mac OS X be a package? Not likely, but possible. If not, how will Mac OS X identify the file type and creator of 'regular' files? By file name extension, that concept so alien to traditional Mac OS? Or will HFS/HFS+-dependent type/creator meta-information solider on into the future? Time will tell.
