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oddiseas

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## Homework Statement

I have just started quantum mechanics bacuase i want to prepare for my class starting in march. I must say so far i find it very confusing: I could use some help with this problem and in addition some explanation on the logic of what it all means.

i get that this theory combines classical mechanics with the wave nature of particles and that the eigenfunctions correspond to standing waves at certain energy levels. But if a particle is localised, what information are we actually getting from its wave function? and how is the wave produced?

Anyway the question i am working on deals with an infinite square well.

Q1)

At t=0 a quantum mechanical system is described by the eigenfunction

[tex]\Psi[/tex]=iA(L-x^2)

-L<=X<=L

a) Clearrly stating your reasons indicate whether or not [tex]\Psi[/tex] is an eigenfunction of the kinetic energy operation;

b) assuming the system is in a well defined eigenstate with total energy E, find the wave function [tex]\Psi[/tex]

## Homework Equations

## The Attempt at a Solution

a)[tex]\Psi_x_x[/tex]=-2iA. This does not match the kinetic operator from schrodingers equation. Anyhow i don't understand what the operator means, so if anyone does i could use some help.

b)Solving for the initial conditions, and then finding A by evaluating the integral of|[tex]\Psi^2[/tex]| i get:

[tex]\Psi_n(x)[/tex]= [tex] \frac{1}{2\sqrt{L}}[/tex]sin(npix/L)

Then i tried using the Fourier series to find the coefficients

but i get something that looks wrong,

i get one value for n=0, a different one for n= even and another for n=odd.

Anyway i don't have the answer to this question and i am getting confused so it would be great if i could see a worked solution.

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