1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Wavefunction in Dirac notation

  1. Nov 16, 2011 #1
    1. The problem statement, all variables and given/known data
    For the infinite square well, a particle is in a state given by [itex] \psi = \frac{1}{\sqrt 2}(\psi_1 + \psi_3) [/itex] , where [itex] \psi_1 [/itex] and [itex] \psi_3 [/itex] are energy eigenstates (ground state and the second excited state, respectively).

    Represent this state as a column matrix [itex] \psi> [/itex] in the energy basis and x basis. You may use your knowledge of the solutions of the infinite square well from before, obtained in the x basis. State with the help of mathematical equations how you would find the column matrix in k basis.

    2. Relevant equations

    I know that in the x-space, the column matrix representation of basis vector is |x> and the components of a state vector [itex] \psi [/itex] is [itex] <x|\psi> [/itex]. And likewise, replace 'x' with 'k' for the k-space basis.

    3. The attempt at a solution

    Is writing [itex] \psi = \frac{1}{\sqrt 2}(\psi_1 + \psi_3)= \frac{1}{\sqrt 2}(<i|\psi_1>+<i|\psi_3>) [/itex] permitted? If not, can you please point me in the right directions? I have Gritffiths Introduction to QM book so any reference to that I can get hold of. Thanks.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted