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Question about Schrödinger equation interpretation

  1. Jan 3, 2013 #1
    1. The problem statement, all variables and given/known data
    Im reading and thinking about the interpretation about Schrödinger equation s solutions (wave functions) - what they realy mean.
    What does the amplitude of wave function correspond to?
    Does it mean that if amplitude is greater then energy of particle is greater as well ?
    I would appreciate any help.
    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 3, 2013 #2

    Simon Bridge

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    Depends what you mean by "really" ;)
    It corresponds to the probability amplitude ... it is it's own thing and does not have a physical meaning by itself. You know that the wave-function, along with it's complex conjugate, form the probability density function for the variable concerned. When you start out you normally have position wave-functions.

    So ##\psi(x)## is the solution to Schrodinger's equation in x.
    ##\psi^\star(x)\psi(x)## is the probability density function for the particle in x.
    ##\int_a^b\psi^\star(x)\psi(x) dx## is the probability of finding the particle with x value between a and b.
    Only this last one has a physical meaning ... the rest are steps in a calculation.

    No. The amplitude is related to probability. In general, the energy is related to the number of anti-nodes in the wave-function ... in free-space, that would be proportional to the frequency.
     
  4. Jan 4, 2013 #3
    Ok,thanks.
    Yes, I was thinkinkg whether the amliptude has a physical interpretation.
     
  5. Jan 4, 2013 #4

    Simon Bridge

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    Only natural.
    It is no more physical than the magnitude of a classical probability density.
    Technically it is more abstract than that - being a step removed. Some people find it a bit spooky - that such abstract ideas can have a physical impact. You'll find some people almost view the abstract math has having a deeper reality than the stuff you can measure.

    Have a look at:
    http://vega.org.uk/video/subseries/8
    ... for a glimpse of how things work.
     
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