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Solving Schroedinger's equation for Step Potential

by uday1236
Tags: equation, potential, schroedinger, solving, step
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Jul8-12, 10:53 PM
P: 3
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 Schrodingerís 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.
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Jul9-12, 06:48 AM
jtbell's Avatar
P: 11,626
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.
Jul9-12, 12:19 PM
P: 3
ok could i forget E was total energy.

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