# Solution to the Schrödinger equation for a non rigid step

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1. Oct 15, 2014

### Arturo Miranda

I've been having troubles resolving the Schödinger's time independent one-dimensional equation when you have a particle that goes from a zone with a constant potential to a zone with another constant potential, yet the potential is a continuos function of the form:

$$V(x)=\left\{ \begin{array}{lcl} 0&\text{if}&x<0\\ \displaystyle\frac{V_{0}}{d}x&\text{if}&0<x<d\\ V_{0}&\text{if}&d<x \end{array}\right.$$

My main problem is around the solution in the second region of the potential, the non-constant region, in which looks like:
$$E\psi(x)=\frac{\hbar^{2}}{2m}d_{x}^{2}\psi(x)+\frac{V_{0}}{d}x\,\psi(x)$$
If tried solving the differential equation by lowering it's order, yet I have not managed to do so. Is there another way of attacking the problem? Or how may I resolve the diff. equation?

2. Oct 16, 2014

### Simon Bridge

3. Oct 16, 2014

### Arturo Miranda

4. Oct 16, 2014

### Simon Bridge

No worries - it's not something you were going to guess.
Note: this sort of thing happens a lot.