Return to Question

We've a potential given as: $V(x)=\left\{\begin{array}{ll}0, & x<0 \\ V_{0}, & x \geq 0\end{array}\right.$. We've got particles coming in from the left towards the step and getting reflected from it. Further, if we assume the energy of the particles coming towards the barrier have lesser energy than the step i.e $E<V$, then it's said that

$T = 0$, The transmission coefficient at a potential step with $E < V$ is zero.

Further it's said that,

The wavefunction in the second region, where $V(x)=V_0$ is $ψ_2(x) = e^{αx}$ where $\alpha=2m(V−E)$.

So we have a probability of finding a particle in the second region even though the transmission at the step is zero!? But this is contradictory. Can anyone please help. Thank you.

We've a potential given as: $V(x)=\left\{\begin{array}{ll}0, & x<0 \\ V_{0}, & x \geq 0\end{array}\right.$. We've got particles coming in from the left towards the step and getting reflected from it. Further, if we assume the energy of the particles coming towards the barrier have lesser energy than the step i.e $E<V$, then it's said that

$T = 0$, The transmission coefficient at a potential step with $E < V$ is zero.

Further it's said that,

The wavefunction in the second region, where $V(x)=V_0$ is $ψ_2(x) = e^{αx}$ where $\alpha=2m(V−E)$.

So we have a probability of finding a particle in the second region even though the transmission at the step is zero!? But this is contradictory. Can anyone please help.

We've a potential given as: $V(x)=\left\{\begin{array}{ll}0, & x<0 \\ V_{0}, & x \geq 0\end{array}\right.$. We've got particles coming in from the left towards the step and getting reflected from it. Further, if we assume the energy of the particles coming towards the barrier have lesser energy than the step i.e $E<V$, then it's said that

$T = 0$, The transmission coefficient at a potential step with $E < V$ is zero.

Further it's said that,

The wavefunction in the second region, where $V(x)=V_0$ is $ψ_2(x) = e^{-αx}$ where $\alpha=2m(V−E)$˙.

So we have a probability of finding a particle in the second region even though the transmission at the step is zero!? But this is contradictory. Can anyone please help. Thank you.

We've a potential given as: $V(x)=\left\{\begin{array}{ll}0, & x<0 \\ V_{0}, & x \geq 0\end{array}\right.$. We've got particles coming in from the left towards the step and getting reflected from it. Further, if we assume the energy of the particles coming towards the barrier have lesser energy than the step i.e $E<V$, then it's said that

$T = 0$, The transmission coefficient at a potential step with $E < V$ is zero.

Further it's said that,

The wavefunction in the second region, where $V(x)=V_0$ is $ψ_2(x) = e^{αx}$ where $\alpha=2m(V−E)$.

So we have a probability of finding a particle in the second region even though the transmission at the step is zero!? But this is contradictory. Can anyone please help. Thank you.

We've a potential given as: $V(x)=\left\{\begin{array}{ll}0, & x<0 \\ V_{0}, & x \geq 0\end{array}\right.$. We've got particles coming in from the left towards the step and getting reflected from it. Further if we assume the energy of the particles coming towards the barrier have lesser energy than the step i.e $E<V$, then it's said that

$T = 0$, The transmission coefficient at a potential step with $E < V$ is zero.

Further it's said that,

The wavefunction in the second region  ,where $V(x)=V_0$ is $ψ_2(x) = Cexp( − αx)$ where $α = 2m(V − E)$˙.

So we've a probability of finding a particle in the second region even though the transmission at the step is zero!? But this is contradictory. Can anyone please help. Thank you.

We've a potential given as: $V(x)=\left\{\begin{array}{ll}0, & x<0 \\ V_{0}, & x \geq 0\end{array}\right.$. We've got particles coming in from the left towards the step and getting reflected from it. Further, if we assume the energy of the particles coming towards the barrier have lesser energy than the step i.e $E<V$, then it's said that

$T = 0$, The transmission coefficient at a potential step with $E < V$ is zero.

Further it's said that,

The wavefunction in the second region, where $V(x)=V_0$ is $ψ_2(x) = e^{-αx}$ where $\alpha=2m(V−E)$˙.

So we have a probability of finding a particle in the second region even though the transmission at the step is zero!? But this is contradictory. Can anyone please help. Thank you.