User Tag List

First 210111213 Last

Results 111 to 120 of 121

  1. #111
    Glowy Goopy Goodness The_Liquid_Laser's Avatar
    Join Date
    Jul 2007
    MBTI
    ENTP
    Posts
    3,377

    Default

    Quote Originally Posted by King-Of-Despair View Post
    This should be fairly simple (hopefully). I haven't been able to solve it after thinking about it and asking a few people:

    Simplify and rationalize:
    (((4+h)^.5) - 2) / h

    I've acquired the answer from the book, but I can't figure out what they did to solve it :\
    Multiply the expression by ((4+h)^.5 + 2)/((4+h)^.5 + 2). After simplifying the expression you should get your answer.
    My wife and I made a game to teach kids about nutrition. Please try our game and vote for us to win. (Voting period: July 14 - August 14)
    http://www.revoltingvegetables.com

  2. #112
    Ruler of the Stars Asterion's Avatar
    Join Date
    May 2009
    MBTI
    INTP
    Enneagram
    5 sp/sx
    Posts
    2,334

    Default

    Quote Originally Posted by The_Liquid_Laser View Post
    Multiply the expression by ((4+h)^.5 + 2)/((4+h)^.5 + 2). After simplifying the expression you should get your answer.
    lol, thanks, I thought of that at one point, but decided that it wouldn't work and didn't actually try it
    5 3 9

  3. #113

    Default

    I wish I could speed teach Calculus, Linear Algebra and Differential Equations... so the Quantum Mechanics could be made plain. It is much simpler than I think people realize.

    Anyone have ideas on how to do that?

    Of course, I could be biased in that I learned classical mechanics first. Teaching that may actually be the more difficult task. This too requires Calculus, Linear Algebra and Differential Equations.

    For those brave enough to attempt a crash course in the three subjects:
    Calculus:
    Definition of a Limit: Limit -- from Wolfram MathWorld
    Definition of a derivative (requires understandning limits): Derivative -- from Wolfram MathWorld
    Definition of an integral (requires understandning limits): Riemann Integral -- from Wolfram MathWorld Wolfram Mathematica Online Integrator
    The fundamental Theorem of Calculus: Fundamental Theorems of Calculus -- from Wolfram MathWorld
    The Second Fundamental Theorem of Calculus: Second Fundamental Theorem of Calculus -- from Wolfram MathWorld
    Taylor and Maclaurin Series: Taylor Series -- from Wolfram MathWorld Maclaurin Series -- from Wolfram MathWorld

    Linear Algebra:
    Matrices: Matrix -- from Wolfram MathWorld
    Vector Spaces:Vector Space -- from Wolfram MathWorld
    Inner Product Spaces:Inner Product Space -- from Wolfram MathWorld
    Orthonormal Bases: Orthonormal Basis -- from Wolfram MathWorld
    Eigenvalues and Eigenvectors: Eigenvalue -- from Wolfram MathWorld Eigenvector -- from Wolfram MathWorld
    Linear Transformations: Linear Transformation -- from Wolfram MathWorld

    Differential Equations (very much cookbook in it's approach, just follow the recepies):
    ordinary differential equations: Ordinary Differential Equation -- from Wolfram MathWorld
    partial differential equations: Partial Differential Equation -- from Wolfram MathWorld
    Fourier Series: Generalized Fourier Series -- from Wolfram MathWorld
    Fourier and Laplace Transforms: Fourier Transform -- from Wolfram MathWorld Laplace Transform -- from Wolfram MathWorld
    Euler Method (Numerical Solution method): Euler Forward Method -- from Wolfram MathWorld
    Runge-Kutta Method (More sophisticated numerical solution method): Runge-Kutta Method -- from Wolfram MathWorld

    Accept the past. Live for the present. Look forward to the future.
    Robot Fusion
    "As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
    "[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
    "[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

  4. #114
    Glowy Goopy Goodness The_Liquid_Laser's Avatar
    Join Date
    Jul 2007
    MBTI
    ENTP
    Posts
    3,377

    Default

    Lol I think you put at least three semester's worth of knowledge into one post.
    My wife and I made a game to teach kids about nutrition. Please try our game and vote for us to win. (Voting period: July 14 - August 14)
    http://www.revoltingvegetables.com

  5. #115
    Senior Member nemo's Avatar
    Join Date
    Jan 2008
    MBTI
    NeTi
    Enneagram
    <3
    Socionics
    wtf
    Posts
    445

    Default

    For QM, I'd add a dash of complex numbers to that list.
    You can't wait for inspiration. You have to go after it with a club. - Jack London

  6. #116
    Glowy Goopy Goodness The_Liquid_Laser's Avatar
    Join Date
    Jul 2007
    MBTI
    ENTP
    Posts
    3,377

    Default

    I've never really looked into QM even though I apparantly have the math background. I guess I'll have to check it out when I get the time.
    My wife and I made a game to teach kids about nutrition. Please try our game and vote for us to win. (Voting period: July 14 - August 14)
    http://www.revoltingvegetables.com

  7. #117
    Senior Member
    Join Date
    Mar 2009
    MBTI
    ISTJ
    Posts
    197

    Default

    Quote Originally Posted by The_Liquid_Laser View Post
    Lol I think you put at least three semester's worth of knowledge into one post.
    It's 5 courses worth of math.
    Calculus I, II, III
    Linear Algebra
    Differential Equations.

    Of course, no sane person can take them all at the same time.

  8. #118

    Default

    Quote Originally Posted by ygolo View Post
    I wish I could speed teach Calculus, Linear Algebra and Differential Equations... so the Quantum Mechanics could be made plain. It is much simpler than I think people realize.

    Anyone have ideas on how to do that?
    This is quite true. People have a habit of wowing and mystifying things.

    I'll try to contribute to this later in the week. I think I can simplify most of it for people, if I find some motivation. Haven't used my brain properly for a while.
    Freude, schöner Götterfunken Tochter aus Elysium, Wir betreten feuertrunken, Himmlische, dein Heiligtum! Deine Zauber binden wieder Was die Mode streng geteilt; Alle Menschen werden Brüder, Wo dein sanfter Flügel weilt.

  9. #119
    Glowy Goopy Goodness The_Liquid_Laser's Avatar
    Join Date
    Jul 2007
    MBTI
    ENTP
    Posts
    3,377

    Default

    Quote Originally Posted by Ozz View Post
    It's 5 courses worth of math.
    Calculus I, II, III
    Linear Algebra
    Differential Equations.

    Of course, no sane person can take them all at the same time.
    It's closer to three, because under the Calculus section the topics really only describe the first semester of Calculus plus some infinite series thrown in.
    My wife and I made a game to teach kids about nutrition. Please try our game and vote for us to win. (Voting period: July 14 - August 14)
    http://www.revoltingvegetables.com

  10. #120
    Senior Member Scott N Denver's Avatar
    Join Date
    Apr 2009
    MBTI
    INFP
    Enneagram
    4w5
    Posts
    2,899

    Default

    Quote Originally Posted by noigmn View Post
    This is quite true. People have a habit of wowing and mystifying things.

    I'll try to contribute to this later in the week. I think I can simplify most of it for people, if I find some motivation. Haven't used my brain properly for a while.
    To quote a math grad student "quantum mechanics is pretty easy, its all just a linear [vector?] space". I heard a QM prof say essentially the same thing.

    1) infinite-dimenionsal linear vector space [ie Hilbert space]
    2) solve a modified wave equation for the particular potential [V] under question. the solution is your wave function psi, or at least a part of it [add spin or other things as needed]. this will amount to PDE, ODE, BVP type problems dealing with the Schrodinger equation
    3) the construct psi star psi serves as your probability density. As a mathematical note from probability theory we assert normalization, ie the integral of psi star psi over all relevant space =1. That way when we multiply two ormore things together we still get 1 x 1...=1.
    4) to compute any quantity of physical interest we compute the expectation value, [which from probability theory?] is integral [psi star * relevant operator representing quantity of interest* psi] integrated over all of relevant space. note: the allowed energy levels are an exception to the above, they come out of the SE itself. but x, x^2, p, p^2, E, etc are computed as expectation values

    5) there are mathematical nuances that are relevant and can be shown, but are kinda just details for this discussion.

    Overall operating motto "1) identify the potential V, 2) solve the relevant schrodinger equation to find the wave function psi 3) compute all physical quantities of interest via <psi, A, psi> where A is the operator for the physical quantity of interest

    I don't know if I made things easier or harder, but there you go.

Similar Threads

  1. The Every-Member-Of-MBTIc Appreciation Thread
    By spirilis in forum The Fluff Zone
    Replies: 18
    Last Post: 10-18-2008, 10:21 PM
  2. The Everyone-Who's-Not-a-Member-of-MBTIc Appreciation Thread
    By ThatsWhatHeSaid in forum The Fluff Zone
    Replies: 5
    Last Post: 10-17-2008, 02:35 PM
  3. MBTIc Appreciation Thread
    By ThatsWhatHeSaid in forum The Fluff Zone
    Replies: 49
    Last Post: 10-16-2008, 02:19 PM

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
Single Sign On provided by vBSSO