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  1. C

    Heisenberg Model

    Homework Statement Find density of states H = \frac{-JzM}{g\mu_B} \sum_i S_i^z + \frac{JzNM^2}{2g^2\mu_b^2} = -\alpha \sum_i S_i^z + \gamma[/itex] z = # nearest neighbors J = exchange M = magnetization S^z = project of total spin S=0,1. Homework Equations Z=\sum_{S m_s} <S m_s|...
  2. C

    Coupled Oscillator

    Homework Statement One mass m constrained to the x-axis, another mass m constrained to the y-axis. Each mass has a spring connecting it to the origin with elastic constant k and they are connected together by elastic constant c. I.e. we have a right-angle triangle made from the springs with...
  3. C

    Lagrange - Mass under potential in spherical

    Homework Statement A particle of mass m moves in a force field whose potential in spherical coordinates is, U = \frac{-K \cos \theta}{r^3} where K is constant. Identify the two constants of motion of the system. The Attempt at a Solution L = T - V = \frac{1}{2} m (\dot{r}^2 + r^2...
  4. C

    Write Lagrangian of spring-mass system

    Homework Statement Spring-mass system on a frictionless surface. A pendulum hangs from the mass of the spring-mass system. Write the Lagrangian. The Attempt at a Solution Take x as the stretch from equilibrium of the spring and k its elastic constant. M is the mass on the spring. Take...
  5. C

    Molecular Vibrations - Numerical

    Homework Statement I'm trying to do some numerical stuff with vibrations of H20 and I'm working in mdyne, angstroms, atomic mass units, and angles are given in radians. What would the corresponding unit of time be when I calculate my normal mode frequencies? femtosecond, 10e-15?
  6. C

    Small Osc. Pendulum+Springs

    Homework Statement Three pendulums hand side-by-side and have there masses connected horizontally via springs. All lengths and masses are equal. Find the Lagrangian and put it in terms of "natural units". The Attempt at a Solution T = 1/2 m l^2 (\dot{\theta_1}^2 + \dot{\theta_2}^2 +...
  7. C

    Coaxial Speed of Propagation

    I know my impedance minima and their associated frequencies for a particular coaxial cable. How would I go about deriving an equation that will let me calculate the speed of propagation and the dielectric constant? My only hint is to consider the case for which Z = 0 but I don't know where to...
  8. C

    Small Oscillations

    A horizontal arrangement with 1 spring in between the two masses, 1 spring connecting each mass to opposite fixed points: k 3m k 8m k |----[]----[]----| I solved the eigenvalue/eigenvector problem for the dynamical matrix D where V = 1/2 D_{ij} w_i w_j and the w's are...
  9. C

    H Fine structure

    Can anyone point me to a reliable (preferably online) resource that states the two Hydrogen red lines due to fine structure?
  10. C

    Speed up a image alignment function using FFT

    Homework Statement I need to speed up a image alignment function using FFT Homework Equations FFT, correlation coefficient (for deciding best alignment) The Attempt at a Solution This function works but a fail to see how it is any better that a naive evaluation of the correlation...
  11. C

    Velocity Dependent Potential

    Homework Statement Consider a particle of mass m and charge q that moves in an E-field \vec{E}=\frac{E_0}{r}\hat{r} and a uniform magnetic field \vec{B}=B_0\hat{k}. Find the scalar potential and show the vector potential is given by \vec{A}=\frac{1}{2}B_0 r \hat{\theta}. Then obtain the...
  12. C

    Lab - Resistivity of Ge

    Resistivity of Ge I'm doing this lab and haven't taken any SS physics so I'm expected to pick up some of the theory on my own. I am having trouble explaining the resistance vs temperature curve for n-type and p-type Germanium, i.e. why does resistance increase and then drop from around 290 K...
  13. C

    Action integral

    Homework Statement Show the stationary value of, J = \int_{a}^{b} dt~L(...;x_i;\dot{x}_i;...;t) subject to the constraint, \phi(...;x_i,\dot{x}_i;...;t) = 0 is given by the free variation of, I = \int_{a}^{b} dt~F =...