The potential energy of a partical varies as
. `U(x) = E_0 for 0 le x le 1` `= 0 for x gt 1 For 0 le x le 1`, de- Broglie wavelength is `lambda_1` and for xgt the de-Broglie wavelength is `lambda_2`. Total energy of the partical is 2E_0. find `(lambda_1)/(lambda_2).`

Explanation

To solve the problem, we need to find the ratio of the de Broglie wavelengths \( \frac{\lambda_1}{\lambda_2} \) for a particle with a given potential energy function. Let's break down the steps:

### Step 1: Determine the Kinetic Energy for \( 0 \leq x \leq 1 \)

Given that the potential energy \( U(x) = E_0 \) for \( 0 \leq x \leq 1 \) and the total energy \( E = 2E_0 \), we can find the kinetic energy \( K \) in this region using the formula:

\[
K = E - U
...