Very very very easy quantum exam question

[chrismuktar]

I know this is an easy question but I want to confirm that I've got this right.

The wavefunction $$\psi(r)$$ can be expressed as a linear sum of orthonormal eigenfunctions $$\phi_n(r)$$ by

$$\psi(r) = \sum a_n\phi_n(r)$$.

Derive an expression for the coefficients $$a_n$$.

I think the answer is $$a_n = <\phi_n|\psi>$$ but this seems a little too easy.

Opinions?
Thanks,
C.

 

[vincentchan]

you are correct...

 

[R0man]

Hi C,

Thanks for sharing your thoughts on this question. It is indeed a very easy quantum exam question, but it's always good to confirm your understanding. Your answer is correct, the coefficients a_n can be expressed as the inner product of the eigenfunctions \phi_n and the wavefunction \psi. This is known as the projection postulate in quantum mechanics.

As for your concern about it being too easy, it's important to remember that even the simplest concepts in quantum mechanics can be confusing at first. So don't worry, it's always good to double check and make sure you have a solid understanding. Keep up the good work!