- #1

xicor

- 37

- 0

## Homework Statement

Show that the following wave function eigenfunction decomposition is viable and find it's expected energy.

ψ(x, t) = [1/(1+i)]ψ1(x)e^(-iw1t) - (1/√2)ψ2(x)e^(-iw2t)

## Homework Equations

∫ψ(x)*ψ(x)dx = 1 probability

∫ψm(x)*ψn(x)dx = 0 orthogonality

∫ψm(x)*ψn(x)dx = δmn

Ʃ|C[itex]_{n}[/itex]|[itex]^{2}[/itex] = 1

<H> = Ʃ|C[itex]_{n}[/itex]|[itex]^{2}[/itex]*E[itex]_{n}[/itex]

## The Attempt at a Solution

From my understanding so far, δmn is value given when you combine the condition for both probability and orthogonality. However I don't think I fully understand why you can just then said that the sum of the constants squared of the wave functions is equal to 1. Using the equation I can find that the first part of wave function is 1/2 and the second part is 1/2 so the sum of that is 1 so the wave function is viable. However I'm not sure what to do with the expected energy. I think that ω = En/h but I am unsure as to how the linear combination effects the expression of expected energy because shouldn't <H> =En since the sum of the constants is just 1?

Thanks for everyone that helps.