Recent content by arpon

  1. arpon

    I Form factors and Interaction term of the Action

    Consider, two fields interact with each other and the interaction term of the action is given. Now the Lagrangian density is fourier transformed and the interaction term of the action is expressed as an integral over the momentum space. How is the integrand related to the form factor?
  2. arpon

    I Transformation of Lagrangian

    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...
  3. arpon

    Green's function of a PDE

    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.
  4. arpon

    Green's function of a PDE

    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}...
  5. arpon

    Two successive rotation (Goldstein problem 4.13)

    I was looking for a rigorous derivation.
  6. 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...
  7. 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.
  8. 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.
  9. arpon

    Velocity of a piston in a piston-shaft mechanism

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

    Velocity of a piston in a piston-shaft mechanism

    You forgot to upload the figure.
  11. 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...
  12. arpon

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

    Isn't the Hamiltonian Operator in the Schrodinger's time dependent equation is the Hamiltonian operator defined for the particular system we are considering?
  13. arpon

    I Experiment: Spin Rotation Operator

    How do we experimentally apply the operator ## \exp{\left(-i\phi\frac{ S_z}{\hbar}\right)}## on a quantum mechanical system? (Here ##S_z## is the spin angular momentum operator along the z-axis) For example, on a beam of electrons?
  14. arpon

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

    Yes. I just wanted to show that the energy eigenkets are also eigenkets to the operator ##i\hbar \frac{\partial}{\partial t}##.
  15. arpon

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

    Can't ##H:=-\frac{\hbar ^2}{2m} \frac{\partial ^2}{\partial x^2} + V(x) ## act on ##\Psi (x,t)## as well?
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