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  1. AlexChandler

    Question about the use of group theory in QM

    I am currently in my second undergraduate quantum course and just finished studying the addition of angular momenta. I am also in my third abstract algebra course and am now covering product groups and group actions. In my QM book (griffiths) there was a reference made to group theory. it said "...
  2. AlexChandler

    Splitting Field Proof

    Homework Statement Consider f(x) = x^3-5 and its splitting field K = Q(5^{1/3}, \omega) where \omega = e^{2 \pi i/3} Show that B = \{1, 5^{1/3}, 5^{2/3}, \omega, \omega 5^{1/3} , \omega 5^{2/3} \} is a vector space basis for K over Q. The Attempt at a Solution I am just a bit...
  3. AlexChandler

    Proof about Constructibility of complex numbers

    Homework Statement Show that if p is prime and e^{2 \pi i/p} is constructable then p=2^k+1 for a positive integer k Homework Equations e^{i \theta} = Cos \theta + iSin \theta The Attempt at a Solution By definition, a complex number a+bi is constructible if a and b are...
  4. AlexChandler

    Proof about hermitian operators

    Homework Statement This is something ive been trying to prove for a bit today. My quantum mechanics book claims that the following two definitions about hermitian operators are completely equivalent my operator here is Q (with a hat) and we have functions f,g \langle f \mid \hat Q f \rangle...
  5. AlexChandler

    Delta Function Bound State

    Homework Statement A particle moves in one dimension in the delta function potential V= αδ(x). (where that is an 'alpha' ... not 'a') An initial wave function is given \Psi = A(a^2-x^2) for x between -a and a and Psi=0 anywhere else What is the probability that an energy measurement will...
  6. AlexChandler

    A Proof involving the GCD and divisibility

    Homework Statement If two integers a and b are relatively prime and if each divides an integer n, prove that their product ab divides n Homework Equations 1=sa+tb for some integers s and t (thm 1.35) gcd(a,b)=1 n=aa'=bb' The Attempt at a Solution I have tried many many different ways...
  7. AlexChandler

    Simple question about partial derivatives

    I have come to a bit of a misunderstanding with partial derivatives. I will try to illustrate my problem. Say we have a function f(x, y(x), y'(x)) where y'(x)=dy/dx. Now suppose that f does not explicitly depend on x. My physics book says at this point that ∂f/∂x=0, even though y(x) and y'(x)...
  8. AlexChandler

    Need advice on my Fall schedule

    Hello, I am a math and physics double major and a junior at Michigan State University. I have already taken introductory physics, the first semster of classical mechanics, a course in thermodynamics and modern physics, and linear algebra (along with the basic calculus and diff eq courses) I...
  9. AlexChandler

    Preparing to Study Quantum Mechanics

    Hello, I will be taking two semesters of quantum physics this year, and am looking for a good book to read before the fall semester to give me somewhat of a head start. Two books I am currently considering are Vol 3 of the Feynman Lectures, and Principles of Quantum Mechanics by Paul Dirac...
  10. AlexChandler

    Proof about primes and gcd

    Homework Statement prove that p is prime iff for any integer "a" either (a,p)=1 or p divides a (where (a,p) denotes the gcd of a and p) Homework Equations (a,b)= the greatest common factor of a and b The Attempt at a Solution I had no trouble with proving the forward direction...
  11. AlexChandler

    Help with a proof on divisibility

    Homework Statement Prove the following: If 5 divides a^2 + b^2 + c^2 then 5 divides a and 5 divides b and 5 divides c. Homework Equations 5 \mid a \implies a=5k , k \in Z The Attempt at a Solution My idea is to assume 5 divides a^2 + b^2 +c^2 also assume that "5 does not divide a"...
  12. AlexChandler

    A Probability tree diagram

    Homework Statement Suppose that the four inspectors at a film factory are supposed to stamp the expiration date on each package of film at the end of the assembly line. John, who stamps 20% of the packages, fails to stamp the expiration date once in every 200 packages; Tom, who stamps 60% of...
  13. AlexChandler

    Proof by Induction

    Homework Statement Prove by induction on n that 11^n - 4^n is divisible by 7 for all natural numbers n (not including zero). Homework Equations Principle of mathematical induction. The Attempt at a Solution Of course I start by showing that the statement holds for n=1 11^1...
  14. AlexChandler

    Proof: Linear Independence

    Homework Statement Let V be a vector space and \{v_1,...,v_{n+1} \} \subset V a set of linearly independent vectors of V . Show directly: (Don't just quote a theorem!) (a) The set \{v_1,...,v_{n} \} is linearly independent. (b) v_{n+1} \not \in span \{v_1,...,v_{n} \} Homework...
  15. AlexChandler

    Counterfeit Coins

    There are seven stacks of coins, each consisting of 100 coins. You know that real coins weigh 10 grams, but counterfeit coins weigh 11 grams. You have an analytical scale that is accurate to .1 gram. Each stack consists of either all real coins or all counterfeit coins, none of the stacks...
  16. AlexChandler

    A Physics Puzzle: Double Circular Motion

    Describe a simple way to force a particle to move along two different circular trajectories at the same time. (Two circles that are not concentric) Hint: The trajectories do not have to be measured from the same frame of reference. It need not be an elementary particle (could be even a small ball)
  17. AlexChandler

    Childhood Persuasive Essays

    I just had a thought that seems somewhat significant, so I thought I'd share it. The structure of most "arguments" that make up the flimsy backbone of pseudoscience very much remind me of the type of arguments that I, and all other children in my school, were encouraged to make in english...
  18. AlexChandler

    Bead Parabola Accelerometer

    Homework Statement An accelerometer is made of a piece of wire with a bead on it that can slide on the wire with no friction. The wire is formed as a parabola y = kx2, as shown in the drawing. The bead rests at the lowest point of the parabola when it is at rest. When accelerated parallel to...
  19. AlexChandler

    Question about Double Slit Experiment with Electrons

    In my modern physics course we learned that electrons, when shot through two close together slits, will produce an interference pattern just light light. However, when you set up an experiment to observe which slit the electron goes through, there is no longer an interference pattern. To my...
  20. AlexChandler

    History of Science Education

    I was wondering if anybody knows about the way in which science was studied in the past. For example, did the great scientists that we read about (Kepler, Galileo, Newton, Euler, Maxwell, Einstein, Dirac... etc) study Math and Physics in similar ways as we? Did they learn by solving example...
  21. AlexChandler

    Momentum Conservation

    Homework Statement I am having trouble with part B of this problem N people, each of mass mp, stand on a railway flatcar of mass mc. They jump off of one end of the flatcar with velocity u relative to the car. The car rolls in the opposite direction without friction. (a) What is the final...
  22. AlexChandler

    A Centrifugal Pump and Angular Momentum

    Homework Statement I have attached a copy of the homework as there is also a picture of the pump. This problem is number 6. A centrifugal pump processes j = 18m3/min of water, with inlet and outlet velocities of v = 15m/s. The impeller rotates in the clockwise direction around the...
  23. AlexChandler

    Air Resistance and Projectile Motion

    Homework Statement An object is ejected straight up into the air at an initial velocity v0. (a) Determine the time for reaching the maximal elevation when the object is subject to gravity alone. (b) Determine the time for reaching the maximal elevation when the object is subject to gravity...
  24. AlexChandler

    Radiation Emission and Absorption

    Homework Statement A sphere of radius 0.500 m, temperature 27.0°C, and emissivity 0.850 is located in an environment of temperature 77.0°C. At what rate does the sphere (a) emit and (b) absorb thermal radiation? (c) What is the sphere's net rate of energy exchange? Homework Equations...
  25. AlexChandler

    Expand Sin(x) about Pi/4

    Homework Statement Expand sin x about the point x = pi/4. Hint: Represent the function as sin x = cos (y + pi/4) and assume y to be small Homework Equations Taylor Series Expansion f(x)= f(a) + f'(a) (x-a)+ (1/2!) f''(a) (x-a)^2+ (1/3!) f"'(a) (x-a)^3+.....+ 1/n! f(n)(a) (x-a)^n The...
  26. AlexChandler

    Preparation for Thermodynamics & Modrn Physics

    Preparation for "Thermodynamics & Modrn Physics" Hello, I will be transferring to Michigan State University next semester (from Washtenaw Community College) and will be taking a course called "PHY 215: Thermodynamics & Modern Physics", which is actually in the Chemistry Building. I have...
  27. AlexChandler

    Setup of a differential element on a propellor blade

    Homework Statement I was looking through my notes, and I saw that my professor solved a propellor blade problem in a way that I don't understand. I took this class two semesters ago, so I cannot ask the professor himself. The problem that I am having is with his setup of a differential element...
  28. AlexChandler

    A Math Puzzle Who can solve it first?

    Here's a little puzzle that I thought of earlier. I gave it to my roommate and he wasn't able to solve it without a pretty good hint, but I'm sure somebody here will get it. |A|+|B| = 2 |A+B| = √(2) What are A and B? (The bars are absolute value signs, and the " √(2) " is the square...
  29. AlexChandler

    How many credits should I take?

    Hello, After this semester I will have completed Math up to Elementary Diff Eq, and both freshman level Calculus based Physics courses. I will be transferring to a university from community college next semester. I am currently taking 20 credit hours: Physics 2, Bio 101, Chem 1, Geography and...
  30. AlexChandler

    Wondering which Math Class to take next

    Hello Everybody I am a Physics Major transferring to Michigan State University next semester. I have completed Calculus based Physics 1 and 2, as well as Calculus 1,2,3, Linear Algebra, and Differential Equations. I am wondering which kind of math class some of you may recommend to take next...
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