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If the class contribute to this page, I would be happy to help by commenting on your contributions.

I think an important concept is to understand the stationary state solutions. solving the time independent schrodinger equation will give us an infinite set of solutions. To get the general wave function we multiply each solution by the corresponding e^-iEt/h (each stationary state has its own allowed value for the energy); we use the Fourier's trick and equation 2.31 to get Cns. Finally we add all the solutions to get the general wave function. I think this is important because when we have the solutions for the time independent schrodinger function, getting everything else (expectation values for x and p and…) is straight forward.

More on separable solutions 2.1 Why use separable solutions?

  1) Separable solutions
       a)Stationary states
           a2) Probability densities and expectation values are time independent
       b)Definite total Energies
           a) that is σ=<H^2>-<H>^2=E^2 - E^2=0
       c) The general solution is a  LINEAR COMBINATION of separable solutions

2.2 INFINITE square well

   1) analyze Shro. eq. @ each boundary i.e. V(x)=0
       a) This leads to the En(eigen value)possible for any n-state.
       b) From this analyze u can readily determine the general solutions for the wave inside of the well.
          a)General prop. of that wave
            
          

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