Old quantum theory The main tool was Bohr–Sommerfeld quantization, a procedure for selecting out certain discrete set of states of a classical integrable motion as allowed states. These are like the allowed orbits of the Bohr model of the atom; the system can only be in one of these states and not in any states in between. The theory did not extend to chaotic motions. Basic principles[edit] The basic idea of the old quantum theory is that the motion in an atomic system is quantized, or discrete. where the are the momenta of the system and the are the corresponding coordinates. are integers and the integral is taken over one period of the motion at constant energy (as described by the Hamiltonian). In order for the old quantum condition to make sense, the classical motion must be separable, meaning that there are separate coordinates in terms of which the motion is periodic. Examples[edit] Harmonic oscillator[edit] a result which was known well before, and used to formulate the old quantum condition. . . and . as
Tesla Turbine: Engine of the 21st Century? The Tesla Turbine could far surpass the efficiency of the internal combustion engine. Recuperative hydraulics can be used for low-speed, high-torque needs. by Sterling D. AllanPure Energy Systems NewsCopyright © 2007 MUNISING, MICHIGAN, USA -- Nikola Tesla created an engine design nearly 100 years ago that is as much as three or four times more efficient than the combustion engine design that has dominated for reasons other than science. At the time of his invention around 1909, Tesla was able to demonstrate a fuel efficiency of 60% with his bladeless turbine design. The politics of his day impeded Tesla's design from being implemented. Enter Environmental Scientist, Ken Reili , CEO of Phoenix Navigation & Guidance, Inc. Rieli and his associates in the popular Phoenix Turbine Builders Club that he founded, have resurrected and improved Tesla's Turbine design. In addition to transportation, potential applications range from home generators to public utilities to locomotive power. Modern Data
Interference (wave propagation) Swimming Pool Interference[1] Interference of waves from two point sources. Magnified-image of coloured interference-pattern in soap-film. The black "holes" are areas where the film is very thin and there is a nearly total destructive interference. Consider, for example, what happens when two identical stones are dropped into a still pool of water at different locations. Geometrical arrangement for two plane wave interference Interference fringes in overlapping plane waves A simple form of interference pattern is obtained if two plane waves of the same frequency intersect at an angle. It can be seen that the two waves are in phase when and are half a cycle out of phase when Constructive interference occurs when the waves are in phase, and destructive interference when they are half a cycle out of phase. and df is known as the fringe spacing. The fringes are observed wherever the two waves overlap and the fringe spacing is uniform throughout. A point source produces a spherical wave. for to where
BirdCam, Round Two In the October 2013 issue, I described the hardware and software I used to create my "BirdTopia Monitoring Station", more commonly called BirdCam. If you've been visiting BirdCam recently, which a surprising number of folks have been doing, you'll notice quite a few changes (Figure 1). In this article, I describe the upgrades, the changes and some of the challenges along the way. If you like fun projects like these involving Linux, please read on and join in my birdy obsession! Figure 1. BirdCam has changed a lot. Slicing and Dicing One of the first changes I wanted to make to BirdCam was to zoom in a bit on the feeders. convert /dev/shm/original.jpg -crop 640x360+1800+1425 \ /dev/shm/birdbath.jpg convert /dev/shm/original.jpg -crop 1920x1080+220+130 \ /dev/shm/birdbath.jpg -gravity southeast -composite \ /dev/shm/final.jpg Figure 2. In the code snippet above, I crop out the small birdbath photo from the original camera photo and save it as birdbath.jpg. Time and Temp The WindowCam
Bra-ket notation In quantum mechanics, bra–ket notation is a standard notation for describing quantum states, composed of angle brackets and vertical bars. It can also be used to denote abstract vectors and linear functionals in mathematics. It is so called because the inner product (or dot product on a complex vector space) of two states is denoted by a ⟨bra|ket⟩, consisting of a left part, ⟨φ|, called the bra /brɑː/, and a right part, |ψ⟩, called the ket /kɛt/. The notation was introduced in 1939 by Paul Dirac[1] and is also known as Dirac notation, though the notation has precursors in Grassmann's use of the notation [φ|ψ] for his inner products nearly 100 years previously.[2][3] Bra–ket notation is widespread in quantum mechanics: almost every phenomenon that is explained using quantum mechanics—including a large portion of modern physics — is usually explained with the help of bra–ket notation. Vector spaces[edit] Background: Vector spaces[edit] though the coordinates are now all complex-valued. where
SciPY for Scientists In my last article, I looked at NumPY and some of its uses in numerical simulations. Although NumPY does provide some really robust building blocks, it is a bit lacking in more sophisticated tools. SciPY is one of the many Python modules that build on NumPY's. To start, you need to import the main scipy module. import scipy This imports the common set of functions and objects used in SciPY. from scipy import signal The simplest package in SciPY probably is the constants sub-package. Linear algebra is one of the heavy uses of computational code. from scipy import linalg linalg.solve(A,b) In many physics and engineering problems, you need to find eigenvalues and eigenvectors. Most people default to using R to do statistics, but you don't have to. stats.ttest_1samp(x, m) where x is your data and m is your model. A topic near and dear to my heart is solving differential equations. Last, but not least, let's look at the weave sub-package.
Hamiltonian (quantum mechanics) The Hamiltonian is the sum of the kinetic energies of all the particles, plus the potential energy of the particles associated with the system. For different situations or number of particles, the Hamiltonian is different since it includes the sum of kinetic energies of the particles, and the potential energy function corresponding to the situation. By analogy with classical mechanics, the Hamiltonian is commonly expressed as the sum of operators corresponding to the kinetic and potential energies of a system in the form where is the potential energy operator and is the kinetic energy operator in which m is the mass of the particle, the dot denotes the dot product of vectors, and Although this is not the technical definition of the Hamiltonian in classical mechanics, it is the form it most commonly takes. which allows one to apply the Hamiltonian to systems described by a wave function Ψ(r, t). The formalism can be extended to N particles: The general form of the Hamiltonian in this case is:
Hack and / - Wiimote Control If you think about it, there are almost as many ways to interface with your computer as there are Debian-based distributions—and that's a lot. Besides the trusty keyboard and optical mouse, there are trackpoint mice, touchpads, touchscreens, twiddlers, joysticks, presentation remotes and even devices that measure your brain waves. Although I mostly stick with my tried-and-true keyboard and trackpoint mouse (fingers on home row, thank you), when I started hearing about all the interesting things people were doing with the Wiimote (the main controller from the Nintendo Wii), I knew I had to give it a try. Now traditionally, connecting a brand-new device to a Linux machine was an investment in Internet research, kernel module hacking, prayer and obscure programming skills I haven't used since college. First, your kernel needs the uinput module available and loaded. KERNEL=="uinput", GROUP="plugdev" Then, I made sure my user was a member of the plugdev group. Use the Wiimote as a Mouse
Fun with E-Ink, X and Gumstix I'm excited by E-paper and the promise it holds. You've probably already heard about E-Ink's E-Paper Display (EPD) and seen it in recent E-book reader products. The E-Ink display media needs no power to hold an image, and it reflects light just like real paper. I've even seen recent products that make use of the physical flexibility of the E-Ink film in order to create “rollable” displays. E-paper devices have been on the market since around 2006 or so. The AM200 kit serves to provide proof of concept for E-Ink. First, let's do a quick review of the hardware infrastructure we're using to better understand the software we need to add. Now, let's dig in to the software side of things. When your Gumstix board arrives, it could have one of two possible firmware configurations. The new software building block that we'll add to this system is something called deferred IO. Okay, now we can do some real work. Connected. The user name is root, and the password is gumstix. . Success!