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## Homework Statement

An electron is confined to an infinite potential well of width L. Find the force it exerts on the walls of the well in the lowest energy state:

a) Estimate the force using uncertainty principle

b) Calculate the force exactly for the ground-state wavefunction

## Homework Equations

[tex]\Delta[/tex]x = L

[tex]\Delta[/tex]x * [tex]\Delta[/tex]p [tex]\geq[/tex] [tex]\frac{hbar}{2}[/tex]

[tex]\Delta[/tex]E * [tex]\Delta[/tex]t = [tex]\frac{hbar}{2}[/tex]

## The Attempt at a Solution

I used the uncertainty principle to solve for [tex]\Delta[/tex]p and [tex]\Delta[/tex]t and divided to get F=dp/dt = (mc^2)/L. I'm not sure if this is correct. I actually didn't really have much of a start until I started typing this up just now.

For part b: I'm not sure what the ground-state wavefunction is. Does this mean k = 1?

I have Schrodinger's equation for 1D, the Hamiltonian, and Hermite polynomials, but don't really know where to begin to relate it all back to force.

Another question:

## Homework Statement

Normalize the wavefunction u(x) proportional to sin(pi*x/L) + sin(2pi*x/L) for a particle of mass m bound in an infinitely deep one-dimensional potential well extending from x = 0 to x = L.

## Homework Equations

1 = A^2 Integral u(x)^2 dx

## The Attempt at a Solution

So I want to solve for A by integrating the u(x)^2 dx from 0 to L since the probability of finding the particle outside of the well is zero. I found a solution online that states A = (2/L)^(1/2) but I keep calculating the integral to be L resulting in A = (1/L)^(1/2). What am I missing?

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