Finite Well and Schrodinger's Equation

[yayz0rs]

Homework Statement

An electron is trapped in a finite well of width 0.5 nm and depth of 50 eV. The wavefunction is symmetric about the center of the well (x = 0.25 nm). If the electron has energy 29.66 eV and ψ(0) = 1.42 (nm)-1/2, then what is the probability for finding the particle in the left half of the well (0 < x < 0.25 nm)?

Homework Equations

Schrödinger's Equation in the classically forbidden zone: C₁e^kx + C₂e^-kx

The Attempt at a Solution

My idea was that because the probability density from negative infinity to .25 nm (L/2) would be .5, I could simply find p(<0) by integrating Schrödinger's equation and subtracting that from .5. However I cannot find K.

I know the equation for K is $$\sqrt{2m/(h/2\Pi)^2(U-E)}$$ and it seems like I've been given those 4 variables. However my homework will not accept my answer for K. For reference I've been getting k = 9.25 nm^-1.

 

[collinsmark]

Hello yayz0rs,

Welcome to Physics Forums.

I'm getting a different answer for k.

My solution to Shrodinger's equation in that region matches yours (at least involving k). There's nothing wrong with your equation for k, as far as I can tell. But still I'm getting a different value than yours when calculating the number.

For your reference, your value for k is different from mine by close to a factor of $$\sqrt{2 \pi}$$. Are you sure you are squaring the $$2\pi$$ along with the h? Are you making sure to use the correct value for h (as opposed to $$\hbar$$ which as the $$2 \pi$$ already factored in)?

 

[collinsmark]

By the way, your equation, as it is written, could use a little clarity by adding parenthesis or something appropriately. In my last post, above, I assume your equation really means

$$k = \sqrt{\frac{2m}{\hbar^2}(U-E)}$$

where

$$\hbar = \frac{h}{2\pi}$$

in which case, we both got the same equation for k.