Solving Schroedinger's equation for Step Potential

  1. Consider the case for a particle with energy E in a region where :
    V = 0 , x<0; V=Vo, x>0;
    for the first region when we write Schrodinger’s equation(Time independent) it will be
    -h^2/2m d2ψ/dx2 = Eψ

    and for second region it was
    -h^2/2m d2ψ/dx2 = (Vo-E)ψ;


    My doubt is that wont the Energy E be different in the second region because the particle experiences an impulse at x=0.

    The case is where E<Vo.
     
  2. jcsd
  3. jtbell

    Staff: Mentor

    The potential energy U and the kinetic energy E - U are of course different in the two regions, but the total energy E is the same everywhere, by conservation of energy.
     
  4. ok thanks....how could i forget E was total energy.
     
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