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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

    Thanks for your insight. I may have misled you into thinking I needed to the differential equations because I asked for the Lagrangian. I'm trying to get the normal mode frequencies by solving the eigenvalue problem. I was thinking your trick might help still but it seems \theta drops out of...
  3. 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...
  4. C

    Write Lagrangian of spring-mass system

    T = \frac{1}{2}(M+m)\dot{x}^2 + \frac{1}{2}m(l^2 \dot{\theta}^2 + 2 \dot{x} l \dot{\theta} \cos \theta) V = \frac{1}{2} k x^2 - m g l \cos \theta I want to find the normal mode frequencies. How do I handle the \cos \theta factor in the kinetic energy matrix when constructing the eigenvalue...
  5. C

    Lagrange - Mass under potential in spherical

    Energy function/Hamiltonian? \frac{\partial L}{\partial t} = 0 = - \frac{dH}{dt} So H = constant.
  6. 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...
  7. 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...
  8. C

    Molecular Vibrations - Numerical

    Thanks for your help -- I'll keep working at it
  9. C

    Molecular Vibrations - Numerical

    Oops I misread the conversion for mdyne. The unit of time is, >> sqrt(1.66e-27*1e-10/1e-8) ans = 4.07430975749267e-015 and the resulting wavenumbers, 2788.1297896707 0 0 0 2709.85261638262...
  10. C

    Molecular Vibrations - Numerical

    For the unit of time calculation I get >> (1.66e-27*1e-10/1e-11)^(1/2) ans = 1.28840987267251e-013 Now, my intention was to convert the \omega values from the eigenvalue problem from [rad/whatever] to [rad/s]. Then I was using the speed of light in [cm/s] to convert these angular...
  11. C

    Molecular Vibrations - Numerical

    Here is how I'm setting up my eigenvalue problem: I know how to construct the G matrix elements. Here's how I construct the F matrix elements: V(Q_1, Q_2, Q_3) = \sum_{i,k,j} K_{i,k,j} (Q_1)^i (Q_2)^j (Q_2)^k K_{i,k,j} can be obtained from this table: i j k Kijk Units 2 0 0 4.227 mdyne °A−1...
  12. 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?
  13. C

    Small Osc. Pendulum+Springs

    No I mean I get \omega^2_1 = 0,~\omega^2_2 = 3/m l^2, ~\omega^2_3 = 1/ m l^2 From -.375 m l^2 \omega+.500 m^2 l^4 \omega^2-.125 m^3 l^6 \omega^3=0 I don't really get the idea of the natural units. Is it just convenience, i.e. solve the eigenvalue problem and then convert back?
  14. 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 +...
  15. 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...
  16. C

    Small Oscillations

    I'm not sure how to go about doing that... How is what I did different than solving (V-\omega^2 T)\cdot \vec{a}=0 for eigenvalues \omega_1,\omega_2? i.e. where T is constructed form the KE and V matrix is constructed from the PE, and is similar to my dynamical matrix D above.
  17. 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...
  18. C

    H Fine structure

    Thanks, the hyperphysics link has what I need: 656.272 120 3 -> 2 Red 656.2852 180 3 -> 2 Red
  19. C

    H Fine structure

    I checked wikipedia I didn't the two lines due to fine structure, only the Balmer series.
  20. 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?
  21. 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...
  22. C

    Velocity Dependent Potential

    Thanks I got them
  23. C

    Velocity Dependent Potential

    Thanks. Wouldn't \dot{z} be the conserved quantity?
  24. C

    Velocity Dependent Potential

    My attempt at corrections (Note the change in coordinate labels): Using cylindrical coords (\rho, \theta, z), L=T-V=\frac{1}{2}m \left ( \dot{\rho}^2+\rho\dot{\theta}^2+\dot{z}^2 \right) - e\phi + e\vec{v} \cdot \vec{A} L = \frac{1}{2}m \left ( \dot{\rho}^2+\rho\dot{\theta}^2+\dot{z}^2...
  25. 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...
  26. 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...
  27. 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 =...
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