- #1
Domnu
- 178
- 0
So let's say we have a particle in the delta function potential, [tex]V = - \alpha \delta(x)[/tex]. I calculated that the reflection coefficient (scattering state) is
[tex]R = \frac{1}{1 + (2 \hbar^2 E/m\alpha^2)}[/tex]
Now, clearly, the term [tex]2 \hbar^2 E/m\alpha^2[/tex] is very small, as [tex]\hbar^2[/tex] has an order of magnitude of [tex]-68[/tex]. This value is so small that even for classical ordered values for [tex]E, m,[/tex] and [tex]\alpha[/tex], the reflection coefficient is very close to [tex]1[/tex]. Is this correct? It seems a bit strange to me that a spike in the potential where a particle's energy is above the potential causes the particle to reflect BACK almost 100% of the time... it seems as if a tank shell going at more than a mile per second goes over a cliff and reflects back...
[tex]R = \frac{1}{1 + (2 \hbar^2 E/m\alpha^2)}[/tex]
Now, clearly, the term [tex]2 \hbar^2 E/m\alpha^2[/tex] is very small, as [tex]\hbar^2[/tex] has an order of magnitude of [tex]-68[/tex]. This value is so small that even for classical ordered values for [tex]E, m,[/tex] and [tex]\alpha[/tex], the reflection coefficient is very close to [tex]1[/tex]. Is this correct? It seems a bit strange to me that a spike in the potential where a particle's energy is above the potential causes the particle to reflect BACK almost 100% of the time... it seems as if a tank shell going at more than a mile per second goes over a cliff and reflects back...