Recent content by arpon

  1. arpon

    I How can we transform a Lagrangian to obtain a new set of equations of motion?

    Consider a Lagrangian: \begin{equation} \mathcal{L} = \mathcal{L}(q_1\, \dots\, q_n, \dot{q}_1\, \dots\, \dot{q}_n,t) \end{equation} From this Lagrangian, we get a set of ##n## equations: \begin{equation} \frac{d}{dt}\frac{\partial \mathcal{L}}{\partial \dot{q}_i} - \frac{\partial...
  2. arpon

    Green's Function for a Partial Differential Equation

    This will transform the PDE into a wave equation. But this exercise asks to solve this problem not using this coordinate transformation. Thanks for your suggestion anyway.
  3. arpon

    Green's Function for a Partial Differential Equation

    Homework Statement Find out the Green's function, ##G(\vec{r}, \vec{r}')##, for the following partial differential equation: $$\left(-2\frac{\partial ^2}{\partial t \partial x} + \frac{\partial^2}{\partial y^2} +\frac{\partial^2}{\partial z^2} \right) F(\vec{r}) = g(\vec{r})$$ Here ##\vec{r}...
  4. arpon

    Two successive rotation (Goldstein problem 4.13)

    I was looking for a rigorous derivation.
  5. arpon

    Two successive rotation (Goldstein problem 4.13)

    Homework Statement Suppose two successive coordinate rotations through angles ##\Phi_1## and ##\Phi_2## are carried out, equivalent to a single rotation through an angle ##\Phi##. Show that ##\Phi_1##, ##\Phi_2## and ##\Phi## can be considered as the sides of a spherical triangle with the angle...
  6. arpon

    Velocity of a piston in a piston-shaft mechanism

    If ##\frac{d\theta}{dt} = 0## and ##\omega## is nonzero, will the piston move? What do you think? Drawing diagrams may help.
  7. arpon

    I Interpretation of photons having zero spin

    Photon has spin 1 and Higgs boson has spin 0. (Source: Wikipedia) You may find this thread on spin 0 particle helpful.
  8. arpon

    Velocity of a piston in a piston-shaft mechanism

    Why didn't you consider ##\omega## in your solution?
  9. arpon

    Velocity of a piston in a piston-shaft mechanism

    You forgot to upload the figure.
  10. arpon

    I Energy operator and the Hamiltonian operator: Are they same?

    Let $$\Psi(x,t) = A(t) \psi(x)$$ Applying Schrodinger's Time dependent equation: $$\begin{equation} i\hbar\frac{\partial}{\partial t}\left(A(t)\psi(x)\right) = H\left(A(t)\psi(x)\right) \end{equation}$$ Let ##\psi(x)## is an eigenfunction of ##H## with eigenvalue ##E##. So, we get...
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