Recent content by kelly0303

  1. K

    I Direction of an ionized electron's travel

    Hello! If I have an atom traveling with a given velocity and I ionize it in flight, will the electron remain at the place of ionization, or it will travel at the same speed along with the resulted ion? Thank you!
  2. K

    I Spontaneous symmetry breaking from a QM perspective

    The Hmiltonian is in the link I sent (well the Lagrangian)... It's equation 11.108.
  3. K

    I Spontaneous symmetry breaking from a QM perspective

    It's equation 11.108 in the link I sent (I guess you're fine with me not literally copy-pasting that here).
  4. K

    I Spontaneous symmetry breaking from a QM perspective

    That's exactly what I am saying. In SSB, the 2 states (please see the link in the above post) that are symmetric with respect to the center should not be eigenstates, as they don't respect the symmetry of the Hamiltonian (hence the name of SSB). Yet in that plot (on page 362) I see no energy...
  5. K

    I Spontaneous symmetry breaking from a QM perspective

    Griffiths introduces a 1D spontaneous symmetry breaking, describes it and then moves to the 2D case. So I am confused why is this 1D case not a real SSB?
  6. K

    I Spontaneous symmetry breaking from a QM perspective

    I am not sure I understand. How is the 1D more symmetric than the 2D? The local maxima looks symmetric in both cases, while the valleys don't. Why do we have SSB in 2D?
  7. K

    I Spontaneous symmetry breaking from a QM perspective

    Thank you for this! I was actually confused by that. As I mentioned before the SSB was introduced in my particle physics class as a 1D (I think it is in Griffiths, too). Then we extended it to 2D. I didn't see any flaws in the calculations (but I was just introduced to it), so what is exactly...
  8. K

    I Spontaneous symmetry breaking from a QM perspective

    I am not sure I understand what you mean. Check what?
  9. K

    I Spontaneous symmetry breaking from a QM perspective

    Oh, no no, I totally agree. If the tunneling probability is very close to zero a state that is non-stationary in theory is basically stationary in practice for timescales as long as the age of the universe. My questions is purely theoretical now: as I said in my last post, if they are not...
  10. K

    I Spontaneous symmetry breaking from a QM perspective

    Thank you for this! Ok so stuff that I am still confused: In the spontaneously symmetry breaking case, why can't the 2 states tunnel from one to another? I assume that the tunneling probability is very law, but I don't see why it would be zero. So if it is not zero, it means that there is an...
  11. K

    I Spontaneous symmetry breaking from a QM perspective

    So in the one dimensional case, with a big hill in between, the 2 degenerate eigenstates are stationary states?
  12. K

    I Spontaneous symmetry breaking from a QM perspective

    Can't you make a 1D version? I remember this is how it was introduced first time in my particle physics class. Of course it has no counterpart in the real world, but it is a valid theoretical system, isn't it? But actually now I am confused about basic QM based on the first reply (regardless of...
  13. K

    I Spontaneous symmetry breaking from a QM perspective

    But my questions still remains. Do the stationary states have or not the same symmetry as the Hamiltonian (which means that in that basis the off diagonal terms are zero)? If they don't, then the 2 lowest energy states in the Mexican hat potential are not stationary (as they don't have the...
  14. K

    I Spontaneous symmetry breaking from a QM perspective

    One more thing. I read this article and on page 2 it states: "the state of a system, if it is to be stationary, must always have the same symmetry as the laws of motion which govern it". But if I understand it right from your reply: "the ground states are not symmetric under the symmetry...
  15. K

    I Spontaneous symmetry breaking from a QM perspective

    I am still confused then, in relation to the ammonia example (not sure if you got to look over my link). In that case we have 2 states (with the N atom being on top or bottom of the plane created by the H atom) in which the system choses a preferential direction, but both having the same energy...
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