Recent content by Juan Carlos

  1. J

    Phase shifts for a localized Coulomb and harmonic potential

    Hello, First of all, it would be nice to see explicitly your attempt of the solution. However, I don't think that you should use the power series method to solve the Radial Schroedinger equation at ##r<a##. In this approach, the problem arises once you impose boundary conditions. NOTE: I will...
  2. J

    Small deviations from equilibrium and Lagrange multipliers

    Hello Ted. Looking through your expressions, I guess that you are using the same notation of the book ("Principles of Statistical Mechanics" by Amnon Katz). Two points: What is the expression of your statistical functions ##f##'s? I assume that it should be something like this for system...
  3. J

    A Second Order Differential equation Bessel-type

    Thanks I will try with this "factorization" procedure.
  4. J

    A Second Order Differential equation Bessel-type

    Variation of parameters! I'll give it a try! Thanks
  5. J

    A Second Order Differential equation Bessel-type

    Hello! Im trying to solve this second order differential equation: \begin{equation*} -\dfrac{d^2y}{dx^2}+\dfrac{3}{x}\dfrac{dy}{dx}+(x^2+gx^4+2)y=0 \end{equation*} Any idea? Maybe it could be converted to a Bessel-like equation (?) with an appropriate change of variables. The equation...
  6. J

    Laplace-Beltrami Operator non-curvilinear coordinates

    Homework Statement I have to find the Laplace operator asociated to the next quasi-spherical curvilinear coordinates, for z>0. Homework Equations \begin{align} x&=\rho \cos\phi\nonumber\\ y&=\rho \sin \phi\nonumber\\ z&=\sqrt{r^2-\rho^2}, \end{align} The Attempt at a Solution I computed...
  7. J

    Classical Mechanics: Lagrangian for pendulum with oscillating support

    for sure, there is a total derivated connecting both.
  8. J

    Gauge Freedom Quantum Electrodynamics

    and the reason is? I repeat, equations of motion don't change.
  9. J

    Gauge Freedom Quantum Electrodynamics

    I get your point, is the usual treatment for one particle. But what I'm saying is related to the two particle system, where the question is: Is it correct use two different gauges, one for each particle? Thank you
  10. J

    Gauge Freedom Quantum Electrodynamics

    For Example: Let's suppose we have the magnetic field in the z direction, for example two Landau's gauges: \vec{A_{1}}=B(-y,0,0) and \vec{A_{2}}=B(0,x,0) where both satisfy \vec{B}=B\vec{k} . So in particular I could say that my Hamiltonian for the two particle system is...
  11. J

    Gauge Freedom Quantum Electrodynamics

    It's the standard construction. It's the standard construction.
  12. J

    Gauge Transformation Quantum Electrodynamics

    It's well known when if we are working on problems related to particles in presence of an electromanetic field, the way we state the problem can be done using the next Hamiltonian: H=\dfrac{(p-\frac{e}{c}A)^2}{2m} +e \phi where the only condition for A is: \vec{\nabla } \times \vec{A} =\vec{B}...
  13. J

    Gauge Freedom Quantum Electrodynamics

    It's well known when if we are working on problems related to particles in presence of an electromanetic field, the way we state the problem can be done using the next Hamiltonian: H=\dfrac{(p-\frac{e}{c}A)^2}{2m} +e \phi where the only condition for A is: \vec{\nabla } \times \vec{A} =\vec{B}...
  14. J

    Two level system: tunnel effect

    Hi! I'm having problems with this simple problem: Consider two level system: a box containing one particle, the box is divided by a thin membrane. Let Ψ1 and Ψ2 the probability amplitude (time-dependent only) of being on the left and right side. The particle can tunnel through the partition: so...
  15. J

    Two level system: tunnel effect

    Hi! I'm having problems with this simple problem: Consider two level system: a box divided by a thin membrane. Let
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