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What is the meaning of En^+ or En^-

  1. Nov 2, 2009 #1
    I see in a lot of places things like


    where E stands for the energy, but I don't get what that upperscript + could be. I see both + and - in the upperscript.

  2. jcsd
  3. Nov 2, 2009 #2
    Without the proper context... Maybe they are energies of propagating waves in positive and negative direction (different waveguided modes)?
  4. Nov 2, 2009 #3
    The exercise is the following(note that I am not asking for a solution to the exercise, I just want to know what the + stands for!):

    "An operator U is said to be unitary if U^+ U = U^- U = 1. Prove that if H is hermitian, then exp(iH) is unitary"

    (Can't find at the moment something involving the En^+..that's because I saw it as a resolution to an exercise, not in the problem itself.
  5. Nov 2, 2009 #4
    The + (usually dagger) in that context is the Hermitian conjugate, which, for a matrix, is the complex conjugate of the transpose of a matrix. A matrix is Hermitian if [tex]H = H^\dagger[/tex] and unitary if [tex]U^{-1} = U^\dagger[/tex].
  6. Nov 2, 2009 #5
    I had thought of that, but I can swear it is not a dagger, it is a +!. Although looking in the resolution of the exercise I'd say that in that case it is indeed a dagger. I'll give you another one:

    "Calculate the probability that an energy measurement yields the ground state energy; the energy of the first excited state"

    The resolution then starts with:

    Minimum energy -> n = 1

    P(n=1) = P1 = |A1|
    P1+=|A1+|2, P1-=|A1-|2

    [tex]\Psi[/tex](x,t) = [tex]\sum[/tex]An+Un+(x)Exp(-i/h * En+t) + [tex]\sum[/tex]An-Un-(x)Exp(-i/h * En-t)

    Un+=[tex]\sqrt{2/a}[/tex] Cos(2n-1)PI x / a), Un-=[tex]\sqrt{2/a}[/tex] Cos(2n)PI x / a)
    Last edited: Nov 2, 2009
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