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

[Dassinia]

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 c_n(t)∅n(x) = Ʃ c_n(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).

Homework Equations

The Attempt at a Solution

Nothing, sadly.

Thanks !

 

[ehild]

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 c_n(t)∅n(x) = Ʃ c_n(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).

Homework Equations

The Attempt at a Solution

Nothing, sadly.

Thanks !

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

 

[Dassinia]

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

 

[ehild]

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... ?

Read the question:

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).

What does orthogonality mean? What is the inner product of two eigenfunctions?

ehild

 

[Dassinia]

Solved, it was really trivial.. !
Thanks for your answers !