Solving Schroedinger's equation for Step Potential

[uday1236]

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 won't the Energy E be different in the second region because the particle experiences an impulse at x=0.

The case is where E<Vo.

 

[jtbell]

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.

 

[uday1236]

ok thanks...how could i forget E was total energy.