Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Dirak notation question

  1. Feb 12, 2014 #1
    I have the following question for anyone who can help:
    Suppose in Dirak notation i have the following state:
    /ψ> = 2 /u1> + /u2> where /u1>,/u2> are the two first eigen kets of energy of the infinite square well.

    That means <x/u1>= Asin(π x /L) and <x/u1>= Asin(2 π x /L) which gives :

    <x/ψ>= 2Asin(π x /L) + Asin(2 π x /L)

    Everything ok so far. But what would happen if i chose <x/u1>= - Asin(π x /L) instead of
    <x/u1>= Asin(π x /L) which is perfectly legitimate. Then <x/ψ> would become:

    <x/ψ>= -2Asin(π x /L) + Asin(2 π x /L) which is not the same as

    <x/ψ>= 2Asin(π x /L) + Asin(2 π x /L) ..( you can not get to one another by multiplying a constant phase so the are different)
    So the question is does /ψ> = 2 /u1> + /u2> determine the state of a system or not because it seems that it depends on my free choice of base kets /u1>, /u2> ?
  2. jcsd
  3. Feb 12, 2014 #2
    Yes, that's correct. Any change to the phase of /u1> must be matched with another phase to the coefficients of the expansion of /ψ>, otherwise you will get a different state.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Dirak notation question Date
I Question about charge Wednesday at 3:24 PM
I Confused about Dirac Notation Jan 13, 2018
I Double sided arrow notation in Dirac Field Lagrangian Oct 30, 2017
B Teacher needs help: Bra–ket notation for parabolas? Oct 22, 2017
I Confusion about Dirac Notation (interferometer) Oct 15, 2017