# Quantum - Find the formal expression of the coefficient cn(t=o)

Quantum -- Find the formal expression of the coefficient cn(t=o)

Hello everyone,
I'm really stuck on the first question of an exercise, so I can't start!!

## Homework Statement

ψ(x,t) a wave function normalized and solution of Shrodinger equation for a given potential.
I the eigenfunctions are given by the ∅n(x) (supposed to be a phi) with eigen values En so we can write ψ(x,t) as:
ψ(x,t)=Ʃ cn(t)∅n(x) = Ʃ cn(t=0)e^(-i*En*t/h)∅n(x)

a. Find the formal expression of the coefficient cn(t=o) in terms of ∅n(x), and show the maths of your result by using the orthogonality of ∅n(x).

## The Attempt at a Solution

Thanks !!!!!

ehild
Homework Helper
Hello everyone,
I'm really stuck on the first question of an exercise, so I can't start!!

## Homework Statement

ψ(x,t) a wave function normalized and solution of Shrodinger equation for a given potential.
I the eigenfunctions are given by the ∅n(x) (supposed to be a phi) with eigen values En so we can write ψ(x,t) as:
ψ(x,t)=Ʃ cn(t)∅n(x) = Ʃ cn(t=0)e^(-i*En*t/h)∅n(x)

a. Find the formal expression of the coefficient cn(t=o) in terms of ∅n(x), and show the maths of your result by using the orthogonality of ∅n(x).

## The Attempt at a Solution

Thanks !!!!!

You certainly learnt about the eigenfunctions of a Schrödinger equation???
What does it mean that the eigenfunctions are normal?

For eigenfunctions u(x) we have H*u(x)=E*u(x)
Do you mean that the eigenfunctions are normalized ?

ehild
Homework Helper
For eigenfunctions u(x) we have H*u(x)=E*u(x)
Do you mean that the eigenfunctions are normalized ?

Not only normalized, but also... ?