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# strange\silly Strange/silly problem of Scatteringscattering from a step potential barrier

ItThis is probably a silly question, and have that has no physical meaning, but I want to be sure: Assume

Assume we gothave the potential barrier: $$V(x) = \begin{cases} V_0 & x>0 \\ 0 & x<0 \end{cases}$$ Now assume the particle is coming from the right. Is itthat possible? physicallyPhysically I think not, but mathematically what is making it not possible? Although,

Although it seemsseemed wrong to continue, I wrote down the equations, I and tried to solve it. them:

$$x<0: \ \ \phi_1(x)=Ae^{ik_1x}+Be^{-ik_1x}, k_1=\sqrt{\frac{2mE}{\hbar^2}}$$ $$x>0: \ \ \phi_2(x)=Ce^{k_2x}+De^{-k_2x}, k_2=\sqrt{\frac{2m(V_0-E)}{\hbar^2}}$$
Now from physicalesFrom physical limits:, $$A=0, C=0$$$$A=0$$ and $$C=0$$.

FromAnd from boundary conditions:, $$B=D$$ and $$ik_1=k_2$$ (an equalsequation that I think supportsupports the notion that all the whole thing is garbage).

My question is that a, are these really unmeaningmeaningless, non-physical results as a result that it is not physical or that I'm Wrong? Or am I wrong, and there is a meaningphysically meaningful interpretation of the results?

# strange\silly problem of Scattering from a step potential barrier

It probably silly question, and have no physical meaning, but I want to be sure: Assume we got the potential barrier: $$V(x) = \begin{cases} V_0 & x>0 \\ 0 & x<0 \end{cases}$$ Now assume the particle is coming from the right. Is it possible? physically I think not, mathematically what is making it not possible? Although, it seems wrong to continue, I wrote the equations, I tried to solve it. $$x<0: \ \ \phi_1(x)=Ae^{ik_1x}+Be^{-ik_1x}, k_1=\sqrt{\frac{2mE}{\hbar^2}}$$ $$x>0: \ \ \phi_2(x)=Ce^{k_2x}+De^{-k_2x}, k_2=\sqrt{\frac{2m(V_0-E)}{\hbar^2}}$$
Now from physicales limits: $$A=0, C=0$$

From boundary conditions: $$B=D$$ and $$ik_1=k_2$$ (an equals that I think support that all the thing is garbage).

My question is that a really unmeaning results as a result that it is not physical or that I'm Wrong and there is a meaning?

# Strange/silly problem of scattering from a step potential barrier

This is probably a silly question that has no physical meaning, but I want to be sure:

Assume we have the potential barrier $$V(x) = \begin{cases} V_0 & x>0 \\ 0 & x<0 \end{cases}$$ Now assume the particle is coming from the right. Is that possible? Physically I think not, but mathematically what is making it not possible?

Although it seemed wrong to continue, I wrote down the equations and tried to solve them:

$$x<0: \ \ \phi_1(x)=Ae^{ik_1x}+Be^{-ik_1x}, k_1=\sqrt{\frac{2mE}{\hbar^2}}$$ $$x>0: \ \ \phi_2(x)=Ce^{k_2x}+De^{-k_2x}, k_2=\sqrt{\frac{2m(V_0-E)}{\hbar^2}}$$
From physical limits, $$A=0$$ and $$C=0$$.

And from boundary conditions, $$B=D$$ and $$ik_1=k_2$$ (an equation that I think supports the notion that the whole thing is garbage).

My question is, are these really meaningless, non-physical results? Or am I wrong, and there is a physically meaningful interpretation of the results?

2 deleted 1 character in body

It probably silly question, and have no physical meaning, but I want to be sure: Assume we got the potential barrier: $$V(x) = \begin{cases} V_0 & x>0 \\ 0 & x<0 \end{cases}$$ Now assume the particle is coming from the right (is. Is it possible? physically I think not, mathematically what is making it not possible?) Although, it seems wrong to continue, I wrote the equations, I tried to solve it. $$x<0: \ \ \phi_1(x)=Ae^{ik_1x}+Be^{-ik_1x}, k_1=\sqrt{\frac{2mE}{\hbar^2}}$$ $$x>0: \ \ \phi_2(x)=Ce^{k_2x}+De^{-k_2x}, k_2=\sqrt{\frac{2m(V_0-E)}{\hbar^2}}$$
Now from physicales limits: $$A=0, C=0$$

From boundary conditions: $$B=D$$ and $$ik_1=k_2$$ (an equals that I think support that all the thing is garbage).

My question is that a really unmeaning results as a result that it is not physical or that I'm Wrong and there is a meaning?

It probably silly question, and have no physical meaning, but I want to be sure: Assume we got the potential barrier: $$V(x) = \begin{cases} V_0 & x>0 \\ 0 & x<0 \end{cases}$$ Now assume the particle is coming from the right (is it possible? physically I think not, mathematically what is making it not possible?) Although, it seems wrong to continue, I wrote the equations, I tried to solve it. $$x<0: \ \ \phi_1(x)=Ae^{ik_1x}+Be^{-ik_1x}, k_1=\sqrt{\frac{2mE}{\hbar^2}}$$ $$x>0: \ \ \phi_2(x)=Ce^{k_2x}+De^{-k_2x}, k_2=\sqrt{\frac{2m(V_0-E)}{\hbar^2}}$$
Now from physicales limits: $$A=0, C=0$$

From boundary conditions: $$B=D$$ and $$ik_1=k_2$$ (an equals that I think support that all the thing is garbage).

My question is that a really unmeaning results as a result that it is not physical or that I'm Wrong and there is a meaning?

It probably silly question, and have no physical meaning, but I want to be sure: Assume we got the potential barrier: $$V(x) = \begin{cases} V_0 & x>0 \\ 0 & x<0 \end{cases}$$ Now assume the particle is coming from the right. Is it possible? physically I think not, mathematically what is making it not possible? Although, it seems wrong to continue, I wrote the equations, I tried to solve it. $$x<0: \ \ \phi_1(x)=Ae^{ik_1x}+Be^{-ik_1x}, k_1=\sqrt{\frac{2mE}{\hbar^2}}$$ $$x>0: \ \ \phi_2(x)=Ce^{k_2x}+De^{-k_2x}, k_2=\sqrt{\frac{2m(V_0-E)}{\hbar^2}}$$
Now from physicales limits: $$A=0, C=0$$

From boundary conditions: $$B=D$$ and $$ik_1=k_2$$ (an equals that I think support that all the thing is garbage).

My question is that a really unmeaning results as a result that it is not physical or that I'm Wrong and there is a meaning?

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