How to Express the Wavefunction at t>0?

[moorey6969]

Homework Statement

at t=0 a particle is described by the eigenfunction Ψ(x) given by:
Ψ(x)= iAe^(-x/2) given that x≥0 and 0 given that x<0
where A is a real number.
assuming the system is in a well defined eigenstate with total energy E, write an expression for the corresponding wavefunction.

Homework Equations

The Attempt at a Solution

 

[thebigstar25]

i guess a good start is to note that the wavefunction can be written as a function of x dependence multiplied with a function of t dependence ..

please try and show your attempt of solving the question ..