Wavefunction in Dirac notation

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Homework Statement


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.


Homework 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.



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.
 

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