- #1

Kyuubi

- 16

- 7

- Homework Statement
- A particle of mass m is subject to the potential given below (relevant equations) with V0 > 0.

- Relevant Equations
- \begin{align*}

V(x) = \left\{ {\begin{array}{*{20}{l}}\infty& x < 0\\-V_0&0<x<a\\0&x>a\end{array}} \right.,\\

\end{align*}

I want to verify some inspection I'm making at this problem. Because of the infinite barrier at ##x=0##, we expect the wave function to take the value 0 there to preserve continuity. As such, we can make the conclusion that the wave function will just be a sine term in the [0,a] region.

But looking at the discussion of the finite well in Griffiths' QM, we are basically just taking the odd solution of the finite well, and instead of analyzing the ##x>0## half and saying that the ##x<0## region is replicated with ##-\psi(-x)##, we are just saying that the left half is 0. This is also taking into consideration the fact that the even part of the solution is also not included.

So the solution to this problem should simply just be the odd solution of the centered finite well.

Is this a correct assessment?

Note: I am only interested in the bound states here as of now.

But looking at the discussion of the finite well in Griffiths' QM, we are basically just taking the odd solution of the finite well, and instead of analyzing the ##x>0## half and saying that the ##x<0## region is replicated with ##-\psi(-x)##, we are just saying that the left half is 0. This is also taking into consideration the fact that the even part of the solution is also not included.

So the solution to this problem should simply just be the odd solution of the centered finite well.

Is this a correct assessment?

Note: I am only interested in the bound states here as of now.