Probability of electron in a box problem

[TLeo198]

Homework Statement

Calculate the probability that an electron will be found (a) between x = 0.1 and 0.2 nm, (b) between 4.9 and 5.2 nm in a box of length L = 10 nm when its wavefunction is psi = (2/L)^1/2 sin(2*pi*x/L).

Homework Equations

As far as I know, only the normalization equation, which is A^2 * Integral(psi^2) = 1

The Attempt at a Solution

My problem is actually how to start it. Should I assume that the wavefunction is already normalized, or should I normalize the wavefunction by equating the integral of the squared wavefunction to 1, then solve for A? Sorry if wording of the question is bad. Any help is appreciated.

 

[zhermes]

It looks like the wavefunction is already normalized. Its easy to check.

The fundamental principle of the probabilistic interpretation of quantum mechanics is that the probability of finding a particle between points a and b, is equal to the integral of the wave-function squared over that interval:

$$P(a<x<b) = \int_a^b |\Psi(x) |^2 dx$$

 

[TLeo198]

I was able to solve it, thanks!

 

[mspns]

Given two normalized but non-orthogonal eigen functions, psi=(1/sqrt(pi))exp(-r) and phi=(1/sqrt(3pi))rexp(-r). Construct a new function PSI which is orthogonal to the first function and is normalized.

Can anyone help me please?


Many many thanks for your kind help.

MSPNS