# Force of a particles on a Potential Barrier [closed]

A particle confined by a potential wall exerts some pressure on it. More specifically, suppose that the particle moves in this potential:

$$V(x) ~=~\left\{ \begin{array}{lcc}\text{finite function}&\text{if}& x > b, \\ V_0 &\text{if} &x < b,\end{array}\right.$$ where $V_0 \to \infty$.

In the limit of infinitely high wall, $\psi(b) = 0$, and the force $F$ depends on $\psi'(b)$. The exact expression can be found in the following way:

Derive the expression for $F$ without making any ad hoc assumptions. Let $V_0$ be very large but finite. In this case, you can find the form of the wavefunction $\psi(x)$ in a small neighborhood of $b$ knowing only $\psi'(b)$. Now suppose that the wall shifts by an infinitely small distance $\delta b$. Consider the corresponding change of the potential, $\delta V(x)$, and calculate the variation of energy.

I have tried solving this several other ways, such as $F = -\frac{d E_n}{dL}$ in an infinite square well of length $L$, but I can't get the above to work out.

-
– Qmechanic Nov 5 '12 at 23:24
you in the same class maybe with the above poster? – Dylan Sabulsky Nov 6 '12 at 3:45
Take a look at this for some context: courses.cms.caltech.edu/ph125/midterm.pdf – kendr Nov 6 '12 at 7:50
@kendr, thanks for point that out. Michael, this is not a site for getting people to do your homework problems or especially exam problems for you. – David Zaslavsky Nov 7 '12 at 17:28

## closed as too localized by David Zaslavsky♦Nov 7 '12 at 17:25

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, see the FAQ.