(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the expectation value of position as a function of time.

2. Relevant equations

This is in the latter half of a multi-part question, previously we were given that:

Eqn 1: Ψ(x, t) = A(ψ_{1}(x)e^{−iE1t/h¯}+ iψ_{2}(x)e^{−iE2t/h¯})

and in an even earlier part:

Eqn 2: ψ_{n}(x) = sqrt(2/L)sin(n*pi*x/L)

Note: h¯ = hbar

3. The attempt at a solution

As you can tell, I'm not too awesome at formatting on here so I'm going to quickly explain my method.

I said:

<x> = Integral from 0 to L of Ψ*(x, t)Ψ(x, t) dx

So I told wolframalpha (we're allowed to use it) to simplify Eqn 1, before subbing in Eqn 2.

This gave me:

Eqn 3: -2(ψ_{1}ψ_{2}sin(t(E_{1}-E_{2})/h¯) + ψ_{1}^{2}+ ψ_{2}^{2}

I then subbed in Eqn 2 into Eqn 3 and integrated.

No matter how many times I do this I always end up with a bunch of sines. These sines are all something like sin(n*pi/L) so when I sub in the limits of integration they become sin(n*pi) or sin(0), both of which are 0!

This means that I'm just left with an answer of 2, which is not time dependent.

Can anyone see where I've gone wrong?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Quantum Mechanics - Finding expectation value

**Physics Forums | Science Articles, Homework Help, Discussion**