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Schrodinger and Infinite Square Well hell

  1. Apr 5, 2012 #1
    Schrodinger and Infinite Square Well.... hell

    1. The problem statement, all variables and given/known data
    Show that Schrodinger Equation: [itex]\frac{d^{2}\psi(x)}{dx^{2}}+k^{2}\psi(x)=0[/itex] has the solution [itex]\psi(x)=A\sin(kx)[/itex]

    2. Relevant equations
    [itex]k=\frac{\sqrt{2mE_{tot}-E_{pot}}}{\hbar}[/itex]

    3. The attempt at a solution
    I already know that [itex]\frac{d^{2}\psi(x)}{dx^{2}}+k^{2}\psi(x)=0[/itex] is a differential equation and has a solution [itex]\psi(x)=A\sin(kx)[/itex] but it's just something learnt as fact. How do I go about showing it?

    Any pointers would be appreciated... thanks in advance!
     
  2. jcsd
  3. Apr 5, 2012 #2
    Re: Schrodinger and Infinite Square Well.... hell

    Generally solving differential equations involves knowing general solutions such as the one you've shown. If you wanted to prove it you could just simply sub it into your differential equation and prove that it does indeed satisfy the equation. I.e differential psi twice and add it with (k^2)*psi
     
  4. Apr 5, 2012 #3
    Re: Schrodinger and Infinite Square Well.... hell

    Thank you.. Just needed a kick in the right direction... Didn't even need to use the value of k.
     
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