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

  • Thread starter Dassinia
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  • #1
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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!! :cry:

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).

Homework Equations





The Attempt at a Solution


Nothing, sadly.

Thanks !!!!!
 

Answers and Replies

  • #2
ehild
Homework Helper
15,477
1,854
Hello everyone,
I'm really stuck on the first question of an exercise, so I can't start!! :cry:

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).

Homework Equations





The Attempt at a Solution


Nothing, sadly.

Thanks !!!!!
You certainly learnt about the eigenfunctions of a Schrödinger equation???
What does it mean that the eigenfunctions are normal?
 
  • #3
144
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For eigenfunctions u(x) we have H*u(x)=E*u(x)
Do you mean that the eigenfunctions are normalized ?
 
  • #4
ehild
Homework Helper
15,477
1,854
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
 
  • #5
144
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Solved, it was really trivial.. !
Thanks for your answers !
 

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