Expectation value for a position measurement

[SkyChaser]

Homework Statement

Given the wave function psi(x,0) = 3/5 sqrt(2/L) sin(xpi/L) + 4/5 sqrt(2/L) sin(5xpi/L) in an infinite potential well from 0 to L, what is the expectation value <x> and rms spread delta E = sqrt(<E^2>-<E>^2)

Homework Equations

<x> = integral from 0 to L of psi*xpsi dx

The Attempt at a Solution

I know that the expectation value <E> is just 3/5 E1 + 4/5 E2, however I'm not sure how to find the rms spread of it without cumbersome algebra. And the same with <x>.

 

[TSny]

Hello, SkyChaser.

Your answer for <E> is not correct. Think about what you need to do to the coefficients 3/5 and 4/5 to get the probabilities.

The algebra for the rms spread of E will be less cumbersome if you express E₂ as a multiple of E₁ and then express <E> and <E²> in terms of just E₁.

 

[jtbell]

I'm confused. Your title says "position measurement" but you refer to both x and E. To clarify, which one do you want: <x> or <E>? Δx or ΔE?

 

[SkyChaser]

Both. And yeah, it should be 9/25 E1 + 16/25 E2.